While opposition leaders called for a nationwide strike and prolonged peaceful street protests to demand that the government resign, several thousand people broke away and marched to Yanukovych's nearby office.
A few hundred of them, wearing masks, threw rocks and other objects at police and attempted to break through the police lines with a front loader. After several hours of clashes, riot police used force to push them back.
Dozens of people with what appeared to be head injuries were taken away by ambulance. Several journalists, including some beaten by police, were injured in the clashes.
Opposition leaders denounced the clashes as a provocation aimed at discrediting the peaceful demonstration and charged that the people who incited the storming of the presidential office were government-hired thugs.
Several opposition leaders, including world boxing champion Vitali Klitschko, walked over to Yanukovych's office to urge protesters to return to Independence Square. Order appeared to have been restored by Sunday night, with rows of riot police standing guard behind metal fences.
Some protesters then headed to Yanukovych's residence outside Kiev, but their cars were stopped by police.
Speaking before the vast crowds on Independence Square from the roof of a bus, the opposition leaders demanded that Yanukovych and his government resign.
"Our plan is clear: It's not a demonstration, it's not a reaction. It's a revolution," said Yuriy Lutsenko, a former interior minister who is now an opposition leader.
Chants of "revolution" resounded across a sea of yellow and blue Ukrainian and EU flags on the square, where the government had prohibited rallies starting Sunday. Thousands of protesters remained late into the evening and some were preparing to spend the night on the square.
The demonstration was by far the largest since the protests began more than a week ago and it carried echoes of the 2004 Orange Revolution, when tens of thousands came to the square nightly for weeks and set up a tent camp along the main street leading to the square.
The opposition leaders urged Ukrainians from all over the country to join the protests in the capital.
"Our future is being decided here in Kiev," Klitschko said.
Ukrainian lawmakers meet Monday for consultations and planned to hold a parliament session Tuesday. The opposition is hoping to muster enough votes to oust Prime Minister Mykola Azarov's Cabinet after several lawmakers quit Yanukovych's Party of Regions in protest.
The U.S. Embassy issued a joint statement from U.S. and EU ambassadors encouraging Ukrainians to resolve their differences peacefully and urging "all stakeholders in the political process to establish immediate dialogue to facilitate a mutually acceptable resolution to the current discord."
Protests have been held daily in Kiev since Yanukovych backed away from an agreement that would have established free trade and deepened political cooperation between Ukraine and the EU. He justified the decision by saying that Ukraine couldn't afford to break trade ties with Russia.