Ukrainian opposition protesters pulled down a statue of Lenin in central Kiev as hundreds of thousands took to the streets in the latest display of anger at President Viktor Yanukovich's rejection of closer ties with Europe.

Protesters used ropes to topple the monument, and several then scrambled onto the podium to plant Ukrainian and European flags. Hundreds gathered around to sing the national anthem and chanting "Yanukovich, you're next".

A huge crowd formed, desperate to catch a glimpse of the fallen Bolshevik leader, while passing cars beeped their horns in support. Some took hammers to the fallen statue in an attempt to smash it to pieces and claim souvenirs.

Not everyone approved of the sudden moment of drama, perhaps the most symbolic yet in two weeks of anti-government protest. "They should have got rid of Lenin ages ago, but I'm not sure this is the right way to do it," said Oksana Petrenko. "I've been at the protest for days but we have to avoid it turning violent."

Earlier, the opposition threatened to march on Yanukovych's presidential palace and seal him inside if, in the next 48 hours, he did not sack his prime minister.

Hundreds of thousands crammed into Independence Square and nearby streets on Sunday, chanting "Ukraine is Europe!". They called on Yanukovych to resign in the biggest protest yet of a two-week movement to force the president to reverse a decision to halt European integration.

The protesters carried the yellow-and-blue flags of both Ukraine and the European Union. Although some also waved flags of political parties, the majority of those on the streets were not supporters of particular parties.

One man wielded an effigy of the severed head of the late Libyan leader Muammar Gaddafi above a sign reading: "Vitya [Yanukovych], the game is over!"

"We do not want to be kept quiet by a policeman's truncheon," heavyweight boxer and opposition leader Vitali Klitschko told the crowd.

Since last Sunday, when protesters attempted to storm the presidential administration and riot police responded ruthlessly, there has been no violence. The government has so far taken a hands-off approach to the protests but resisted concessions. The prime minister, Mykola Azarov, survived a no-confidence vote in parliament on Tuesday and branded those on the square "Nazis and criminals", but after previous attempts to clear the square with force increased the protest mood, police withdrew from the city centre.

However, on Friday, Kiev police said that if two occupied buildings in the centre, including the main City Hall, were not vacated within five days, they would be cleared with force.

On Sunday, Eduard Leonov, an MP from the nationalist Svoboda party, was sitting at a desk marked "Committee for the self-government of Kiev" inside City Hall, and described himself as the commander of the building. He insisted that protesters would not acquiesce to the police demands. "First, it's an illegal order, as MPs have the right to hold meetings wherever they want," he said. "Second, it's an immoral order, as this is a humanitarian mission providing food and warmth to the protesters."

Hundreds of mattresses have been laid out on the floor in the City Hall's main colonnaded room, and different stalls hand out food, medicines and donated warm clothes to those who want them.

"It the government decides to storm the building, then of course we will resist," said Leonov.

Yanukovych has kept a low profile since the protests started, even flying to China for a three-day trip last week as the centre of Kiev remained under siege. He returned to Ukraine on Friday, stopping over in Russia to meet with Vladimir Putin, with rumours circling in Kiev that the pair had agreed for Ukraine to join the Russian-led Customs Union. The rumour sparked fury in Kiev but was denied by spokespeople for both presidents.

Russia and the west have traded allegations over which side is putting pressure on Ukraine. On Saturday, former Georgian president Mikheil Saakashvili told the crowd on Independence Square that Putin had performed a "raider attack on a whole sovereign country", attempting to steal Ukraine's fate from its own people.

Alexei Pushkov, the head of the Russian parliament's foreign affairs committee, struck back: "Saakashvili is kind of right. There is an attempted raid on Ukraine, not from Moscow but Brussels, grabbing it by the neck and dragging it to paradise," he tweeted. "The word 'paradise' should be in inverted commas, of course. For Bulgaria, Greece and even for Serbia which is just an EU candidate country, the promised 'paradise' turned to hopeless gloom."

Yanukovych has insisted he still wants integration with Europe, but could not sign the EU deal as it would have caused further damage to Ukraine's suffering economy.