A commander at the rebel-controlled border post southeast of the city of Luhansk said 5,000 people had left by evening, joining a stream he said has continued unabated through a shaky cease-fire set to expire tomorrow.
Tens of thousands of Ukrainians have sought safety in Russia since the fighting began two months ago between government troops and Moscow-backed separatist fighters.
Ukrainian President Petro Poroshenko today called on Russia to support his peace plan "with deeds, not words" as the weeklong cease-fire neared its end in Russian-speaking eastern Ukraine.
The summit also will see Ukraine sign a sweeping trade agreement with the EU that will bind it more closely to the West. It was the former Ukrainian president's sudden decision late last year to back out of the EU deal under pressure from Russia that led to his ouster and triggered the current crisis.
By declaring a cease-fire only through tomorrow morning, Poroshenko may have been trying to push forward the peace process ahead of the EU summit. Russian President Vladimir Putin has urged him to extend the truce and hold talks with the separatists, who have declared independence in the eastern Donetsk and Luhansk regions.
Russian news agencies quoted Andrei Purgin, a leader of the self-proclaimed Donetsk People's Republic, as saying the next round would be held Friday in Donetsk.
Speaking at the Parliamentary Assembly of the Council of Europe in Strasbourg today, Poroshenko urged Moscow to stop the flow of fighters from Russia and take other steps to end the conflict.
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