|"This is the third Sunday in a row that we've seen a giant crowd in the centre of Kiev"|
Protesters, who oppose a customs union with Russia, toppled a statue of Lenin and smashed it with hammers.
This is a kind of replay of the Orange Revolution of 9 years ago. It's all about whether Ukraine forms stronger ties with the EU or with Russia. Most Ukrainians want the relative prosperity that comes with association with the EU, but the President has close ties with Russia and has refused the advances of the EU.
Russian President Putin has long had a desire to rebuild the Russian Federation to it's former CCCP status, and is pulling strings to make sure Ukraine remains closer to them than to the EU. Many Ukrainians simply don't trust Russia or Putin, and with good reason.
But understand this, this is an east vs west power-play that will not easily be resolved.
President Viktor Yanukovych has said he shelved the EU deal after Russian opposition.
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. Then they 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.
One opposition MP, Andriy Shevchenko, tweeted: "Goodbye, Communist legacy!"
Prime Minister Mykola Azarov compared the toppling of the statue to the Taliban's destruction of the giant Buddhas of Bamiyan in Afghanistan in 2001, Interfax-Ukraine news agency reported.
"War on monuments is always barbarity," he said.
The BBC's David Stern says the attack on the statue has heightened tension in Kiev.
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.
The European Commission has said EU foreign policy chief Catherine Ashton will 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 Prime Minister 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," Mrs 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.
Another opposition leader, Oleh Tyahnybok, said: "It's not just a simple revolution. It's a revolution of dignity."
Opposition MP Serhiy Pashynskyy said that "starting from today and until our demands are met, the government quarter will be blocked with protest rallies".
Analysts say that although the protests were sparked by President Yanukovych's U-turn on the EU deal, many on the streets want rid of what they believe is a corrupt system.
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.
Both Russia and Ukraine denied that the issue of Kiev joining the customs union along with Belarus and Kazakhstan came up during the Putin-Yanukovych meeting in Sochi, in southern Russia, on Friday.
Correspondents had earlier speculated that an agreement on Ukraine joining the customs union might be reached in return for reduced energy prices. The two neighbours have also been trying to resolve a long-running dispute over energy supplies.
Ukraine depends on imports of Russian gas, but the supplier, Gazprom, has recently complained that Kiev had fallen behind in payments.
Disputes over supplies to Ukraine before 2009 saw Gazprom temporarily cutting off supplies.
Pipelines passing through Ukraine also pump Russian gas to many EU member states.
"Any signature to a deal on forming a new Soviet Union means the breakup of the country," said Arseniy Yatsenyuk, a prominent opposition member.