The police responded with tear gas.
By early evening, at least one police van was burning on a central street in the city, and witnesses said people had been injured, though it was unclear how severely.
The violence appeared to be the worst in at least a month for the continuing protest movement in Ukraine, and it signified a deepening of the political crisis in the country, the most populous former Soviet state beside Russia.
Protests began in November, after the government of President Viktor F. Yanukovich declined to sign a sweeping free-trade agreement with the European Union.
He later negotiated a financial aid package from Russia.
In speeches on the square, opposition leaders denounced the participants in the melee as provocateurs and said they did not represent the aspirations of the peaceful protesters.
But the leaders were also powerless to stop the fighting.
By midnight, the streets were a scene of utter mayhem.
Those fighting the police struck them with lengths of pipes and sticks, and hurled cobblestones the size of soccer balls into their midst.
They sent fireworks whistling and sparking into their ranks, and threw what appeared to be firebombs, blossoming into flames when they struck.
The police stumbled backward, patting at their clothes as fire burned their metal shields.
The riot police sprayed from a water cannon, in spite of the freezing temperatures.
Gazeta.ru, a Russian news portal, reported that 70 police officers were wounded and 40 hospitalized.
The rally against the new laws enacted on Thursday drew tens of thousands of people, a smaller crowd than at the peak of the protest movement in December but larger than on recent weekends.
Since November, protesters have occupied the square and several buildings, including City Hall.
Protesters said they were angered by laws seen as circumscribing the rights of public assembly.
The laws stiffened the penalties for setting up tents and stages in public spaces.
They banned wearing helmets and balaclavas, a tactic of the opposition activists to protect themselves against the police, identification or arrest.
In defiance, many demonstrators showed up wearing upside-down kitchen kettles on their heads.
The movement’s leaders have struggled to formulate a response to the laws.
Arseniy P. Yatsenyuk, one of the main protest organizers, announced a plan to form a shadow Parliament, government and Kiev city administration that would operate under the laws of a 2004 Constitution that Mr. Yanukovich had amended — illegally, the opposition says.
Late Sunday, Mr. Yatsenyuk, speaking from the stage on the square, said he had received a call from Mr. Yanukovich saying the government was ready for negotiations.
Vitali Klitschko, the leader of Punch, a political party, and a former heavyweight boxing champion, told the crowd that he was “announcing a snap presidential election,” though the parliamentary opposition has no legal grounds to force a vote if Mr. Yanukovich does not resign.
This inability of the leaders to force political change under the current Constitution or consolidate around a single leader in spite of clear popular support for their antigovernment agenda in the capital became a precipitating cause of the violence on Sunday.
A leader of a group of protesters who arrived in a column of cars, a movement called Auto Maidan, after the name of the square, took the stage and said the opposition should choose one leader, and if it could not, the crowd should march on Parliament.
Mr. Yatsenyuk called this speech a provocation to violence.
But some in the crowd acted anyway, moving toward Parliament and clashing with riot police officers.
After the fighting began, Mr. Yatsenyuk, speaking from the stage on the square, called on protesters to refrain from violence and denounced those who were fighting the police, saying they did not represent the opposition.
Source: The New York Times