MOSCOW - Hundreds of thousands of Ukrainians filled the streets of Kiev on Sunday - no longer focused solely on a trade agreement with the European Union, but also turning their attention to recasting their country's frayed and corrupt political system.

The demonstrators represent disparate strains within Ukraine and do not have a cohesive leadership to guide them. They face steep odds in their effort to force embattled President Viktor Yanukovych to resist the heavy pressure that Russia is exerting to keep Ukraine in its orbit.

Yet the sheer numbers demanding closer ties with Europe and a government that listens to its people have pushed the rickety Ukrainian political system closer to the breaking point.

Despite threats of serious criminal charges, columns of marchers expanded their hold on the center of the capital, establishing satellite camps outside Kiev's main square, and toppling a statue of Soviet state founder Vladimir Lenin. They burned firewood in barrels to ward off the cold.

Opposition leaders called on demonstrators to surround all government buildings, at least until Yanukovych fires Prime Minister Mykola Azarov and his cabinet, and new elections are called.

But the government announced that the mostly young occupiers had until Monday to vacate City Hall, where they have set up a headquarters and where it appears a showdown may occur.

More than two weeks of demonstrations on the cold streets of Ukraine's capital - the largest since the country's Orange Revolution in 2004 - have hardened and inspired the protesters. At first, they simply wanted Yanukovych to sign a trade pact with the EU, as he had been promising. Now, they want a new Ukraine - free of corruption, ruled by law, and with honest elections and politicians.

But the various groups in the streets have different political convictions, ranging from liberal to far right. Little unites them beyond a distaste for Yanukovych's government. Their leadership is fragmented, and they lack a pragmatic and achievable agenda.

"Everyone wants the president to go away, but they know it's unrealistic," said Anton Symkovych, professor of sociology at the National University of Kiev-Mohyla Academy. "They need goals, but combating corruption or moving toward Europe aren't clear goals. There are no leaders."

The protesters are young and old, urban and rural. The young - the generation that grew up after the fall of the Soviet Union - make up the largest single group.

"We've always seen Ukraine as independent, and not as a small Russia," said Anastasia Bondarenko, 23, who has been demonstrating every day since Nov. 21. "The protests are transforming people. They're starting to care about problems beyond themselves. They are beginning to self-organize. That is a big change."

When the crowd toppled and beheaded the Lenin statue at one end of Kiev's main avenue, near the venerable Bessarabsky market, police watched but did not intervene. After singing the national anthem, protesters shouted, "Yanukovych, you're next!"

An extremist nationalist organization asserted responsibility for the incident.