Clashes have taken place after large crowds of pro-EU demonstrators rallied in Ukraine’s capital Kiev against new laws restricting public protests.
Stun grenades and flares were thrown as protesters tried to reach parliament, their way blocked by police and buses.
Opposition politician Vitali Klitschko later said President Viktor Yanukovych had agreed to set up a cross-party commission to resolve the crisis.
The US appealed for an end to the violence and urgent political talks.
Mr Klitschko, who leads the Udar party, made comments after meeting President Yanukovych at his residence outside Kiev.
“The president pledged to create on Monday morning a commission with representatives from the presidential administration, cabinet and opposition to find a solution to the crisis situation,” Udar quoted the former world heavyweight boxing champion as saying.
Arseniy Yatseniuk, another opposition leader, said Mr Yanukovych called him to say that he was ready for talks.
The new legislation was passed with a quick show of hands on Thursday by MPs loyal to the president, who then signed it into law.
The opposition accused the ruling party of a coup.
US and EU officials have expressed deep concern at the new legislation.
Ukraine’s current anti-government movement began in protest at Mr Yanukovych’s decision in late November to pull out of a landmark treaty with the EU, but has expanded to demand his resignation.
Sunday’s rally in Kiev, attended by tens of thousands, heard calls from opposition politicians to disregard the new laws curbing protests that pro-EU demonstrators have been staging for the past two months.
Clashes erupted as some people headed away from the main square towards parliament, to vent their anger over the new laws. They ran into police cordons near Kiev’s Dynamo football stadium, some 300 metres from Independence Square.
They pelted police with flares, thunder flashes and petrol bombs, the BBC’s Daniel Sandford in Kiev reports.
They overturned a bus used by riot police and interior troops and set it alight. Other vehicles were also set on fire.
The police could be seen behind buses sheltering under their riot shields, and occasionally throwing their own thunder flashes and gas canisters to try to force the crowd back, our correspondent says.
Police also used water cannon to try to disperse the demonstrators.
Interior ministry spokesman Serhiy Burlakov blamed “provocateurs and extremists” for the confrontations and urged people not to follow their lead.
Police were filming everything and had opened criminal proceedings under Article 294 (organisation of mass riots), the interior ministry said.
The opposition leaders said it was committed to a peaceful resolution of the crisis, denouncing those activists who took part in clashes.
Earlier, Mr Klitschko called on President Yanukovych to respond to the protesters’ demands and to hold elections.
“You’re fighting with your nation. Stop the escalation. Don’t go the way of (former Romanian President Nicolae) Ceausescu and (former Libyan leader Muammar) Gaddafi.
During the day, the rally on the main square heard a call from a former Ukrainian navy chief for members of the armed forces to defy “illegal” orders from those in power, Unian news agency reported.
“Tomorrow the regime will enslave you too. Therefore we are calling on you to fulfil your military oath of loyalty to the Ukrainian people and not to the authorities who have gone off the rails,” said Rear Admiral Ihor Tenyukh, who was sacked by Mr Yanukovych in 2010.
Opposition leaders are under huge pressure to come up with an action plan, amid criticism from many activists that their campaign has been too passive.
The new curbs on protests, which have been signed into law by the president, include:
The protesters have been camping out behind extensive barricades on the Euromaidan, as Independence Square has been dubbed, for nearly two months.
The mass demonstrations were initially triggered by President Yanukovych’s last-minute rejection of an EU deal under heavy pressure from Russia in November.
The protesters’ demands later widened to include the fight against what they said was widespread government corruption and abuse of power.