The decision to leave the border posts came as the government vowed to beef up its security presence to counter pro-Russian rebels amid reports of continued fighting in the country's east.
The three checkpoints, all in the volatile Lugansk region, were targeted in attacks by pro-Russian rebels overnight yesterday to today, the border guards said in a statement.
"After an exchange of fire, the threat to the lives of people crossing the border prompted the evacuation of civilians and border guards at the checkpoints," the statement said.
Numerous civilians were also crossing into Russia on foot with suitcases and bags of belongings, seeking refuge from the hostilities on the Ukrainian side.
"The Ukrainian border guards numbered about 50 and left towards 5 am today," said Vitaly Bliznyuk, the commander of a group of pro-Russian fighters.
"When we got here, we noticed that the border guards had already left and had detonated their ammunition beforehand," he told AFP.
Kiev says combatants are crossing frequently from Russia, some having travelled from the Caucasus region.
Russia says several thousand refugees cross the border in the other direction every day, a claim which Ukraine denies.
"Instead of opening up its borders to all who wish to escape from the combat zone, they have closed it. It's a complete scandal and unacceptable," said Russian foreign ministry spokesman Alexander Lukashevich.
Sporadic gunfire continued across the restive eastern region today, with rebels still controlling key administrative buildings in the main city of Donetsk.
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