Ukraine's acting president, Oleksandr Turchynov, says he is not against a national referendum on what kind of country Ukraine should be.
Mr. Turchynov said Monday he is certain a majority would support a united and independent Ukraine, possibly giving broader localized rights to the east. He said such a vote could be held at the same time as the May 25 presidential election.
In Moscow, Russian Foreign Minister Sergei Lavrov said Monday he believes Russian-speaking Ukrainians in the eastern part of the country should be part of drafting a new constitution.
Pro-Russian demonstrators who have seized Ukrainian government buildings in several cities, including yet another (Horlivka) on Monday, are demanding a referendum on whether to split with Ukraine and join Russia - similar to last month's vote in Crimea.
Eastern Ukraine is on edge as Mr. Turchynov threatens to launch what he called a "full-scale anti-terrorist operation" against those who have taken over the buildings.
However, a Monday morning deadline passed without any sign of movement by security forces against the protesters who remain in place behind barricades in the city of Slovyansk and elsewhere.
Mr. Turchynov has promised amnesty for those who give up their weapons and come out peacefully. But he says he will not let Russia take over eastern Ukraine the way it annexed Crimea.
Russia came under heavy criticism during an emergency meeting of the U.N. Security Council Sunday night.
U.S. Ambassador Samantha Power accused the Russians of "writing and choreographing" the violence in Ukraine.
British Ambassador Mark Lyall Grant says satellite images show as many as 40,000 heavily armed Russian troops massed near the Ukrainian border.
Russia insists it has the right to protect Russian speakers it says are under threat in Ukraine. Russia accuses the interim Ukrainian government of being anti-Russian and anti-Semitic extremists.
Russian Ambassador Vitaly Churkin said the West has the power and the influence to push the Ukrainians towards dialogue and away from force.
Ukraine's Ambassador Yuriy Sergeyev said Russia's comments do not correspond with reality. He called on the Russians to immediately stop violating Ukrainian sovereignty.
Ukrainian special forces and pro-Russian militia exchanged gunfire in the eastern Ukrainian city of Slovyansk Sunday, with both sides reporting casualties. Pro-Russian gunmen had taken over the Slovyansk police station and government facilities in the cities of Donetsk and Kramatorsk.
Top diplomats from Russia, the United States, Ukraine and the European Union are set to hold emergency talks on the crisis April 17 in Geneva. White House officials say U.S. Vice President Joe Biden will travel to Kyiv April 22.