Protesters, who oppose a customs union with Russia, toppled a statue of Lenin and smashed it with hammers.
President Viktor Yanukovych has said he shelved the EU deal after Russian opposition.
Protest leaders have given him 48 hours to dismiss the government.
As darkness fell, protesters were blockading key government buildings with cars, barricades and tents.
Witnesses said a group of protesters toppled the statue of Soviet leader Lenin at the top of Shevchenko’s Boulevard using metal bars and ropes and then began smashing it up with hammers.
Others stood by chanting “glory to Ukraine”.
Correspondents say the statue has symbolic importance as it underlines Ukraine’s shared history with Russia.
In another development on Sunday, the Ukrainian Security Service said it was investigating some politicians on suspicion of what it called “actions aimed at seizing state power”.
It did not name the politicians.
Amid rising tensions, the European Commission said EU foreign policy chief Catherine Ashton would travel to Ukraine this week “to support a way out of the political crisis”.
Waving EU and Ukrainian flags, protesters on Sunday congregated on Kiev’s Independence Square – the scene of previous clashes with police.
Ukraine’s special police force, Berkut, has been widely condemned for beating protesters in the square – known as Maidan.
The opposition party of jailed former PM Yulia Tymoshenko has urged people to “chase” the president “until he falls”.
“We are on a razor’s edge between a final plunge into cruel dictatorship and a return home to the European community,” Yulia Tymoshenko said in a message to the crowd read out by her daughter.
“Don’t give in, not a step back, don’t give up, the future of Ukraine is in your hands,” the message read.
The protests are the largest since the pro-democracy Orange Revolution in 2004.
A smaller pro-government rally was held close to the opposition march with police separating the two.
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