Some 70% of the Russian troops believed to have been in Ukraine have withdrawn back across the border, Ukrainian President Petro Poroshenko said, according to the national news agency Ukrinform.
"This is another hope that peaceful initiatives have a good perspective," Poroshenko is quoted as saying during a Cabinet meeting in Kiev on Wednesday.
The remarks came several days into a shaky ceasefire deal between Ukrainian forces and pro-Russia rebels.
Moscow has repeatedly denied sending any Russian troops over the border into Ukraine.
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Pro-Russia rebels in Ukraine should open a humanitarian corridor for surrounded Ukrainian troops to retreat from the battlefield, the Russian President's office said Friday.
The step comes a day after a U.S. official accused Russia of sending up to 1,000 of its soldiers into southern Ukraine to fight alongside the rebels.
NATO produced what it says are satellite images showing Russian troops engaged in military operations inside Ukraine.
NATO has called an emergency meeting Friday in Brussels, Belgium, at the request of the Ukrainian authorities, a day after the U.N. Security Council was summoned over the crisis.
Russia continues to deny that it is either supporting the rebel forces or has sent its own forces over the border.
Ukrainian troops were fighting on two fronts Thursday: southeast of rebel-held Donetsk, and along the nation's southern coast in the town of Novoazovsk, about 12 miles (20 kilometers) from the Russian border.
Mykhailo Lysenko, the deputy commander of the Ukrainian Donbas battalion, on Thursday described the fighting in the south as "a full-scale invasion."
Analysts suggest that Russia may have sent its forces into Novoazovsk in order to throw Ukrainian forces making gains against besieged rebel forces in the cities of Donetsk and Luhansk onto the back foot.
In a statement issued by the Kremlin, President Vladimir Putin said the rebels had been successful in halting a Ukrainian military operation in eastern Ukraine that he said had endangered the civilian population and caused many casualties.
As a result, he said, they should allow the Ukrainian soldiers - who he said were fulfilling orders, not volunteering - to leave the battlefield, to reunite with their families, get medical help for the injured and avoid more casualties.
The Prime Minister of the self-declared Donetsk People's Republic, Alexander Zakharchenko, said in a televised statement on Russia's state-run Russia 24 channel that the rebels would do so if the surrounded Ukrainian troops agree to hand over their weapons.
Separatist forces in eastern Ukraine, backed by Russian tanks and armored personnel carriers, battled government forces on two fronts Thursday, a Ukrainian military official said.
The fighting was taking place southeast of Donetsk, and along the nation's southern coast in the town of Novoazovsk, about 12 miles (20 km) from the Russian border, according to Mykhailo Lysenko, the deputy commander of the Ukrainian Donbas battalion.
"This is a full-scale invasion," Lysenko said, referring to the fighting in the south.
A day earlier, Ukraine's National Defense and Security Council told reporters that Russian forces were directing massive artillery fire over the border at Novoazovsk.
Russian forces and pro-Russia rebels have seized villages around the town, the NSDC said.
The NDSC also claimed that members of a Russian tactical battalion were present in the village of Pobeda, in Ukraine's Luhansk region.
"If these troops got lost and accidentally found themselves in Ukraine as well, they should go back East," the update said.
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Ukrainian border guards are in Russia and have started to examine the contents of a huge convoy of trucks that Moscow says is carrying relief goods for civilians in war-torn eastern Ukraine, a border guard official said Friday.
The purpose of the procession of trucks, which abruptly changed course earlier this week, has been the subject of dispute between Russia and Ukraine.
The Ukrainian government has expressed fears that the mission is a camouflaged effort to smuggle supplies to pro-Russian rebels and has vowed to keep the convoy out.
Russia insists that it should be permitted to send aid to the conflict-battered region, many of whose residents are Russian speakers.
The Ukrainian government, whose forces have been fighting the pro-Russian rebel groups for months, has said any aid needs its approval and has to go through the Red Cross or the United Nations.
Serhay Astahov, a spokesman for the the Ukrainian border guard service, told CNN on Friday that border guards had started inspecting the trucks at a checkpoint on the Russian side of the border from Ukraine's Luhansk region.
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Ukraine's military announced a one-day cease-fire on Thursday to allow international experts full access to the site where Malaysia Airlines Flight 17 crashed two weeks ago, officials said.
Fighting between the military and pro-Russia rebels in the area of the crash site has repeatedly prevented international monitors and investigators reaching the debris field where human remains and victims' belongings still lie scattered.
World leaders, including U.N. Secretary General Ban Ki-moon have appealed to all parties in the conflict in eastern Ukraine to halt the fighting so that the international teams can do their job.
The statement issued Thursday by Ukraine's Counter-Terrorist Operation's press center said the military would not take offensive action but will "respond to direct attacks."
The statement also accused the rebels of continued violence, including firing Grad rocket systems.
"The Russian militants do not adhere to the international agreements and demands. At 9 a.m. they used two Grad systems to shot in the village of Peremozhne. This demonstrates their attitude towards Ukraine and the international community."
The United States and others say Russia has provided arms to rebels in eastern Ukraine, including heavy weapons such as a missile system like the one believed used to down the Malaysian airliner two weeks ago.
Russia and the rebel fighters deny involvement in the shootdown of MH17.
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A week after Malaysia Airlines Flight 17 was shot down over war-torn eastern Ukraine, dozens more coffins containing remains of victims of the crash were due to arrive in the Netherlands on Thursday.
They will follow the first 40 wooden caskets, which were flown in Wednesday and greeted by somber, moving tributes across the country.
A lone bugler sounding the traditional military farewell "Last Post" marked their arrival at a military base in Eindhoven.
The grieving nation then held a moment of silence to honor those killed in the crash of the jetliner - caught in a war in which they had no part.
The plane was downed last week by a suspected surface-to-air missile over eastern Ukraine, where groups of pro-Russian rebels are battling Ukrainian government forces.
In a reminder of the ongoing bitter conflict, rebels claimed responsibility for shooting down two Ukrainian military jets on Wednesday. The rebels have denied that they brought down Flight 17.
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A train carrying 282 bodies from Malaysia Airlines Flight 17 arrived in Kharkiv, Ukraine, getting the bodies one step closer to their grieving families around the world.
The train arrived at a rail station and continued on to an undisclosed location. The bodies will eventually be taken to the Netherlands.
But a litany of obstacles remain - not just in handling the remains, but in figuring out how and why MH17 was shot down over eastern Ukraine.
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A Malaysia Airlines passenger jet crashed in a rebel-controlled part of eastern Ukraine on Thursday, spurring swift accusations from Ukrainian officials that "terrorists" shot down the aircraft.
The United States has concluded a missile shot down the plane, but hasn't pinpointed who was responsible, a senior U.S. official told CNN's Barbara Starr.
The Boeing 777 with 298 people aboard fell from the sky near the town of Torez in the Donetsk region of eastern Ukraine, officials said. A top Ukrainian official said the plane, which was on the way from Amsterdam to Kuala Lumpur, was flying at about 10,000 meters (nearly 33,000 feet) when the missile hit.
A radar system saw a surface-to-air missile system turn on and track an aircraft right before the plane went down, the senior U.S. official said. A second system saw a heat signature at the time the airliner was hit, the official said. The United States is analyzing the trajectory of the missile to try to learn where the attack came from, the official said.
The Obama administration believes Ukraine did not have the capability in the region - let alone the motivation - to shoot down the plane, a U.S. official told CNN's Jake Tapper.
Malaysian Prime Minister Najib Razak said the plane never made a distress call.
He called for an international team to have full access to the crash site.
"We must and we will find out precisely what happened to this flight. No stone will be left unturned," he said.
"If it transpires that the plane was indeed shot down, we insist that the perpetrators must swiftly be brought to justice," Najib said.
Ukrainian officials maintained that pro-Russian separatists were behind the crash.
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Russia is expected to face new sanctions Monday for its actions in Ukraine, President Barack Obama told reporters in Manila, Philippines.
"The sanctions build on the ones that were already in place. We're moving forward with expanded list of individuals," he said.
The move, Obama said, was to spur Russian President Vladmir Putin to "walk the walk not just talk to talk" in resolving the crisis in Ukraine.
If the latest round of sanctions don't work, the next phase could target sectors like banking, Obama said.
The European Union also is expected to impose sanctions Monday on about 15 Russian officials who are believed to be undermining democracy and creating chaos in Ukraine, according to Western diplomats.
The sanctions will include asset freezes and travel bans.
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U.S. officials Thursday denounced what one called a "grotesque" leaflet ordering Jews in one eastern Ukrainian city to register with a government office, but the Jewish community there dismissed it as a "provocation."
The fliers were handed out by masked men in front the main synagogue in Donetsk, where pro-Russian protesters have declared a "People's Republic," Jewish leaders there said. The document warned the city's Jews to register and document their property or face deportation, according to a CNN translation of one of the leaflets.
Geoffrey Pyatt, the U.S. ambassador to Ukraine, told CNN's "The Lead with Jake Tapper" that a respected Jewish leader in Ukraine showed him a photograph of one of the leaflets. He called the document "chilling."
And in Geneva, where diplomats held emergency talks on the Ukrainian crisis, U.S. Secretary of State John Kerry called the leaflets "grotesque" and "beyond unacceptable."
But the Jewish community statement said relations between the Jews of Donetsk and their neighbors were amicable, and the self-proclaimed head of the "People's Republic," Denis Pushilin, denied any connection to the fliers.
Pushilin told CNN the handwriting on the flier wasn't his, and the title attached to his name was not one he uses. It wasn't clear who had distributed the leaflets, but the chief rabbi of nearby Dnipropetrovsk said, "Everything must be done to catch them."
"It's important for everyone to know it's not true," said the rabbi, Shmuel Kaminezki. "The Jews of Donetsk will not do what the letter says."
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