President Barack Obama has urged Russian President Vladimir Putin to stop the flow of weapons into Ukraine and halt support for separatists.
The White House said that in the phone call Barack Obama warned of further sanctions if Moscow failed to act.
The Kremlin says Vladimir Putin urged direct talks between Kiev and the rebels in the east. Russia denies arming them.
The separatists have said they will observe a truce initiated by Ukrainian President Petro Poroshenko.
The week-long ceasefire – part of a 15-point peace plan announced by Petro Poroshenko last week – is due to expire on Friday.
Late on Monday, White House spokesman Josh Earnest told reporters: “The president spoke to President Putin and once again urged him to support peace instead of allowing the provision of arms and materiel across the border and continuing support for militants and separatists who are further destabilizing the situation in Ukraine.”
“Russia will face additional costs if we do not see concrete actions to de-escalate the situation,” he said.
The US and EU have already imposed a number of sanctions, including visa bans and asset freezes on Russian officials, after Moscow annexed the Ukrainian region of Crimea in March.
Washington said last week that a number of Russian tanks and armored personnel carriers had crossed the border into the east of Ukraine.
The Russian government has strenuously denied that any of its tanks crossed the border into Ukraine.
On Monday, the US State Department said Washington also had new information that tanks were being readied at a site in south-western Russia to be sent into Ukraine.
As diplomatic efforts to ease the crisis continued, Vice President Joe Biden spoke to Ukraine’s President Petro Poroshenko in a phone call on Monday, telling him that the US would continue to strongly support his peace plan, the White House said.
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