Ukrainian police have begun moving against protesters in central Kiev, with some protest camps in front of government buildings dismantled.
An opposition party said security forces had raided its headquarters.
Officials gave protesters until Tuesday to leave. No clashes were 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 the city centre than on Sunday, when hundreds of thousands of people came out onto the streets.
US Vice President Joe Biden spoke over the phone to Ukrainian President Viktor Yanukovych earlier, expressing "deep concern" about the situation in Kiev and urged dialogue with the opposition.
"[Mr Biden] noted that violence has no place in a democratic society and is incompatible with our strategic relationship," the White House said in a statement.
Warning to protesters
Police were seen forcing protesters out of two streets where, according to the Interior Ministry, they were blocking access to administrative buildings.
Some barricades and tents were also removed at at least two sites.
Prosecutor-General Viktor Pshonka warned protesters to stop causing "anarchy and lawlessness" by blocking the buildings.
The ministry said no action was being taken on Independence Square itself.
Demonstrators are now putting up additional barricades on the square.
"We call on people to stand their ground, and peacefully, without using force or aggression, to defend their right to live in a free country," said heavyweight boxing champion Vitaly Klitschko, who has emerged as one of the leaders of the protests, quoted by Reuters news agency.
"We are expecting the break-up by police of peaceful demonstrators. If blood is spilled during this dispersing, this blood will be on the hands of the person who ordered it: ...[President Viktor] Yanukovych."
Meanwhile, spokespeople for the opposition Fatherland Party said security forces were occupying its headquarters and "breaking down doors".
They left after the party's computer servers were seized. The party's website is currently inaccessible.
A police spokeswoman said neither the regular Kiev police nor Berkut riot police had conducted any operations at the address.
Local media said the troops were from the SBU state security service, but the service made no comment on the reports.
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 Yanukovych has said he will discuss the crisis with three former presidents on Tuesday to try to find a compromise.
The protesters have given Mr Yanukovych 48 hours to dismiss the government and are demanding new elections for the presidency and government.
They are blockading government buildings with cars, barricades and tents.
The demonstrators have condemned Mr 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.
EU foreign policy chief Catherine Ashton will be in Ukraine on Tuesday and Wednesday "to support a way out of the political crisis".
Baroness Ashton will hold talks with government officials, opposition activists and civil society groups.
The Commission says the EU's offer of an association agreement with Ukraine remains on the table, provided Ukraine meets the conditions - and they cannot be renegotiated.
Sunday's demonstration was the biggest so far in nearly three weeks, and the biggest in Ukraine since the 2004 Orange Revolution, which swept pro-Western leaders to power.
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.
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.