US Vice President Joe Biden "strongly condemned the violation of the ceasefire by separatist forces acting in concert with Russian forces, in and around the town of Debaltseve", the White House said in a statement on Tuesday after he spoke to Ukrainian President Petro Poroshenko.
"If Russia continues to violate the Minsk agreements, including the most recent agreement signed on February 12, the costs to Russia will rise," the White House statement added.
Ukraine earlier appealed to the West to get "tough" on Russia after pro-Moscow separatists stormed the flashpoint town to attack thousands of government troops, violating the three-day-old ceasefire.
But Russian President Vladimir Putin -- who denies backing Ukraine's insurgency -- said the conflict, which has killed more than 5,600 people, could not be solved by "military means" and urged Kiev's troops to surrender.
"I hope that the Ukrainian authorities are not going to prevent the Ukrainian soldiers from laying down their weapons," Putin said in a press conference during a visit to Budapest.
Poroshenko, in a phone conversation with German Chancellor Angela Merkel, said the assault on Debaltseve was a "cynical attack" on the truce brokered last week by Germany and France.
He called for the European Union and international community to take a "tough reaction against the treacherous actions of the rebels and Russia".
Kiev and pro-Russian rebels agreed a peace roadmap on February 12 after marathon negotiations in Minsk involving the leaders of France, Germany, Russia and Ukraine.
But the insurgents have argued that Debaltseve, which sits on a railway line linking rebel-held Donetsk and Luhansk, is well inside their territory behind the frontline so should not be included in the ceasefire agreement, while Kiev says it controls the territory.
The UN Security Council on Tuesday "called on all parties to immediately cease hostilities" and allow peace monitors to enter the town.
Intense shelling was heard in the Debaltseve area on Tuesday.
Ukrainian officials admitted that pro-Russian rebels had taken parts of the town and surrounded some of the army units there, but said fierce fighting was continuing.

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