Some 70% of the Russian troops believed to have been in Ukraine have withdrawn back across the border, Ukrainian President Petro Poroshenko said, according to the national news agency Ukrinform.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.
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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