Riot police are taking up positions near Kiev’s City Hall, where thousands of Ukrainian anti-government protesters have massed.
More police are being bussed in with priests urging them not to use force.
The tense stand-off follows weeks of demonstrations after a government U-turn on a free trade deal with the EU.
President Viktor Yanukovych said a short while ago he would hold talks involving the opposition on Tuesday.
A statement on the president’s website said Viktor Yanukovych would hold talks with three of his predecessors on Tuesday to try to find a compromise.
The protesters have given Viktor Yanukovych 48 hours to dismiss the government and are demanding new elections for the presidency and government.
They have condemned Viktor Yanukovych for refusing to sign an association agreement with the EU last month. He said he shelved it because it would put trade with Russia at risk.
Protesters are blockading government buildings with cars, barricades and tents.
EU foreign policy chief Catherine Ashton will be in Ukraine on Tuesday and Wednesday “to support a way out of the political crisis”.
President of the European Commission, Jose Manuel Barroso, said in a statement that he had spoken to Viktor Yanukovych over the telephone and asked him “to show restraint”.
Jose Manuel Barroso said he had asked him “to not use force against the people that are demonstrating peacefully, to fully respect the freedoms that are so important for all of us in Europe”.
Hundreds of thousands of people took part in Sunday’s protest – the biggest so far in nearly three weeks of opposition demonstrations in Kiev.
During the evening, a group of protesters smashed the city’s statue of the Russian revolutionary leader Lenin, and brought its dismembered parts as trophies to Independence Square.
The statue stood at the top of Shevchenko Boulevard, and was toppled with metal bars and ropes, then smashed up with hammers. No arrests were reported in the incident.
These are the biggest street protests in Ukraine since the 2004 Orange Revolution, which swept pro-Western leaders to power, though Viktor Yanukovych made a comeback in 2010.
Many of the protesters suspect Russia’s President Vladimir Putin of trying to model a new Russian-led customs union on the Soviet Union. So far only Belarus and Kazakhstan have joined it.
The opposition party of jailed former PM Yulia Tymoshenko has urged people to “chase” the president “until he falls”.
Meanwhile the Ukrainian Security Service said it was investigating some politicians on suspicion of what it called “actions aimed at seizing state power”.