The BBC’s Steve Rosenberg said priests have been blessing riot police
Ukrainian police have begun dismantling protest camps in front of government buildings in Kiev.
An opposition party said the police had also raided their headquarters.
The protesters had been given until Tuesday to leave. No clashes have been reported.
Opposition leaders urged supporters to defend Independence Square, the main protest site. The stand-off follows weeks of unrest after a U-turn on a free-trade deal with the EU.
The BBC’s Steve Rosenberg in Kiev says there are far more police in central Kiev than on Sunday, when hundreds of thousands of people came out onto the streets.
Police were dismantling at least two protest sites and forcing protesters out of two streets where, according to the Interior Ministry, they were blocking access to administrative buildings.
However, the ministry said no action was being taken on Independence Square itself.
Meanwhile spokespeople for the opposition Fatherland Party said police were occupying its headquarters and “breaking down doors”.
However, a police spokeswoman said neither the regular Kiev police nor Berkut riot police had conducted any operations at the address.
The websites for Fatherland and the opposition Freedom Party are currently inaccessible.
Fatherland is the party led by former Prime Minister Yulia Tymoshenko, who was jailed in 2011 over a controversial gas contract with Russia.
Protesters are demanding her release.
President Viktor Yanukovych has said he will discuss the crisis with three former presidents on Tuesday to try to find a compromise.