Pro-Russian separatists occupying state buildings in eastern Ukraine face a Friday deadline imposed by Kyiv to surrender their weapons.
Armed men this week stormed government buildings in Luhansk and Donetsk, demanding Ukraine allow a referendum on independence.
The government has offered amnesty for those who surrender. But it has threatened to use force if the buildings are not vacated by Friday.
Ukrainian Prime Minister Arseniy Yatsenyuk met Friday with local leaders in Donetsk, and said he is optimistic the standoff can be resolved.
"I would like to state clearly that the central government is not only ready for dialogue with regions, but is ready to fulfill lawful requirements and wishes of all the citizens of our country. In the framework of the changed constitution, we will be able to satisfy specific requests of every single region."
There were no immediate signs the government is preparing to follow through on its threats to use force to vacate the buildings. Neither was their evidence the protesters were about to surrender.
In Luhansk, one protester, who did not give her name, said if police attempt to remove the activists, things will only get worse.
"We will stay here until the end. Our children are now working in mines, but when it starts (Ukraine government operation to clear building) they will all come here. We will stay and if they kill us - let it be."
Recent surveys suggest residents of eastern Ukraine overwhelmingly oppose any move to join Russia.
Meanwhile, there are lingering concerns that Moscow may be preparing to invade eastern Ukraine.
NATO on Thursday released aerial photographs showing what it says are 40,000 Russian troops, along with tanks and aircraft massed near the Ukrainian border.
The imagery, released to news outlets, follows repeated Russian assurances the deployment is no cause for alarm.
On Friday, Russian Foreign Minister Sergei Lavrov said he is ready for four-party talks on Ukraine with the U.S., the European Union and Kyiv.
But he said in order for tensions to be reduced, the West should stop its efforts to "legitimize" Ukraine's pro-Western leaders.
"We believe it is indeed possible to de-escalate the Ukrainian crisis. To achieve that, it is necessary to stop imposing fait accompli, to stop the efforts by every possible means, to legitimize the 'Maidan' government."
Ukraine's current government came to power following the so-called "Euromaidan" protests that forced the country's pro-Russian leaders from power in February.
A month later, Moscow proceeded to annex Ukraine's Crimean peninsula, a move that prompted Washington to impose sanctions on Russia.
The U.S. is threatening to impose more economic penalties if Russia does not pull back its troops from the border.
A White House statement on Thursday said the U.S. and its allies are "prepared to meet further Russian escalation with additional sanctions."
At the World Bank/IMF spring meetings in Washington Thursday, U.S. leaders also threatened more sanctions against Russia.
U.S. Treasury Secretary Jack Lew told his Russian counterpart he could expect "significant" sanctions in the event of further escalation.