Russian President Vladimir Putin has said he supports a peace plan tabled by Ukraine - as long as it includes "practical action" to start talks.
He said Kiev must negotiate and make compromises with pro-Russian rebels for the plan to be "viable and realistic".
Putin also said a week-long truce - declared by President Petro Poroshenko - must not be used as an "ultimatum".
Clashes have continued in eastern Ukraine, with rebel attacks overnight injuring six border guards.
The separatist fighters have dismissed the truce, accusing the Ukrainian army of violating their own ceasefire.
Meanwhile, the US has imposed sanctions - including asset freezes - against seven pro-Russian leaders in Ukraine.
A statement issued by the Kremlin on Saturday evening said that the Russian leader supported Poroshenko's ceasefire, "as well as his stated intentions to take a number of concrete steps to achieve a peaceful settlement".
According to the statement, Putin also insisted that the plan would only work if it led to "meaningful negotiations and political compromise between the opposing sides in eastern Ukraine".
Ukrainian forces have struggled to regain control of buildings and territory that have been seized by the armed separatists in eastern regions bordering Russia.
On Friday night, the separatists attacked three Ukrainian border posts in the Donetsk and Luhansk regions, Kiev said.
The rebels shelled the posts with rocket and mortar fire, injuring six border guards. The gunmen also attacked Ukrainian forces outside the Kramatorsk airfield, in the Donetsk region.
Ukrainian forces returned fire, and all the attacks were repelled, Kiev said. However, Ukraine's border guard service said its personnel at the Izvaryne post, Luhansk region, were forced to retreat into Russian territory.
A number of casualties were reported among the separatists.
Poroshenko on Friday declared the ceasefire to give rebels time to disarm. It became effective from 22:00 local time (19:00 GMT).
The president also unveiled proposals for the peace plan involving decentralising power, holding early elections, and creating a 10km (six-mile) buffer zone on the Ukrainian-Russian border.
Rebel leaders have said they will not disarm until government troops have left the east.
Pavel Gubarev, self-styled governor of the "Donetsk People's Republic", said there was no ceasefire near Slovyansk, a bastion of separatist forces.
"There is shooting all the time, and this ceasefire that Poroshenko is talking about is just fake. The Ukrainian forces are either not under his control, or he is just a liar.''
The Kremlin had earlier dismissed the truce, saying it was "not an invitation to peace and negotiations but an ultimatum".
The US and European Union leaders previously imposed sanctions after Russia annexed the Ukrainian region of Crimea in March.
On Friday, the US Treasury Department said it had blacklisted seven rebel leaders, including self-proclaimed mayors, governors and commanders in chief of cities under siege by Ukrainian forces.
Their assets in the US will be frozen and US firms will be banned from dealing with them.
US officials also said "scalpel" sanctions against Russia's defence, finance and high-tech industries were being considered.
Washington says Russia is providing the separatists with military equipment, including tanks, and is building up troops on its border with Ukraine.
Moscow denies the claims.