Russian news agencies on Friday quoted Vasily Malayev, spokesman for the Federal Security Service in the Rostov region, as saying that three crossings east of Donetsk were temporarily closed late Thursday night because of fighting on the other side.
Ukraine says it regained control of one crossing which had been controlled by rebels.
Pro-Russian insurgents in eastern Ukraine have declared independence and have been fighting Ukrainian government troops for more than three months. Government forces have been advancing in the recent days, pushing the insurgents closer to the Russian border.
Malayev told RIA Novosti on Friday customs staffers had been evacuated from the border crossing while border guards remained at their positions.
On Thursday, Kiev launched an all-out attack on pro-Russia strongholds of Donetsk and Lugansk. The move followed recent advances by government forces, which have pushed pro-Russians closer to Ukraine’s eastern borders.
Ukrainian forces regained control of the eastern city of Slavyansk on July 5 following overnight attacks. Andrei Purgin, deputy prime minister of the self-proclaimed Donetsk People’s Republic, said fighters only left Slavyansk to protect the civilian population.
The country's mainly Russian-speaking parts in the east have witnessed deadly clashes between pro-Russia activists and the Ukrainian army since the government in Kiev launched military operations in mid-April in a bid to crush the pro-Russia protests.
Violence intensified in May after the Donetsk and Lugansk regions held local referendums, in which their residents voted overwhelmingly in favor of independence from Ukraine.
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