Explosions are taking place, fireworks are being thrown and large fires have broken out in Independence Square, known locally as the Maidan.
Police have deployed water cannon.
During the day, at least nine people were killed, including two policemen, as protesters and security forces clashed in the worst violence in weeks.
Security forces had earlier given protesters a deadline of 18:00 local time (16:00 GMT) to end the unrest and surrounded Independence Square, which has been the scene of a mostly peaceful protest camp since November.
The city’s metro service was suspended, and there were reports that cars were being prevented from coming in to the capital.
Thousands of people are in the square, which is close to Ukraine’s parliament building.
Opposition leader Arseniy Yatsenyuk had insisted the protest camp would “not retreat a single step from here, from this Maidan”.
“We have nowhere to retreat to, Ukraine is behind us, and Ukraine’s future is ahead of us. No fear, only faith in our strength, only solidarity and unity, only mutual support.”
Protest leader Vitaly Klitschko had urged women and children to leave the square, saying he could not “exclude the possibility of use of force”.
Shortly before 18:00 GMT, police announced over loudspeakers that they were about to begin “an anti-terror operation”.
Then they began firing water cannon at protesters and advancing with an armoured vehicle. Protesters lit fires and appeared to be throwing fireworks.
Large numbers of people are still in the square and appeared from TV footage to not be leaving.
In a speech from the stage Mr Yatsenyuk, who leads the Fatherland party, appealed to President Viktor Yanukovych to “call off your chain dogs who are shooting at civilians”.
“There are people here, children, youth and women. We did not start this confrontation. We are urging you to pull the law-enforcement bodies back 200 metres. Stop the bloodshed and call a truce until morning,” he said, in a speech broadcast on Ukraine’s News 24 channel.
“We are talking about human lives and the future of the country which could be drowned in blood. Stop, Viktor Yanukovych, stop.”
An aide to Mr Yanukovych was quoted by Ukrainian media earlier as saying the president was “against confrontation and conflict” and did not want to forcibly disperse the Maidan camp.
Ukraine’s unrest began in November, when President Yanukovych rejected a deal with the EU in favour of closer ties with Russia.
Pro-EU protesters are demanding his resignation and snap elections.
After weeks of unrest, the mood had calmed in recent days, but the protest camps remained in place.
Then earlier on Tuesday, police blocked protesters from marching on parliament, where MPs had been due to debate proposed changes to the constitution which would have reduced the powers of the president.
The debate did not take place. Mr Yatsenyuk said President Yanukovych was blocking the reforms and that his allies “show no desire whatsoever to end the political crisis”.
But MPs who support the president said the proposals had not been thoroughly discussed, and that more time was needed.
Some protesters outside parliament ripped up cobblestones to throw at police. Others threw smoke bombs. Police fired stun and smoke grenades, and rubber bullets.
Protesters also attacked the headquarters of President Yanukovych’s Party of the Regions, temporarily smashing their way in and setting it on fire before being forced out by police.
At least seven protesters were killed along with two policemen who officials said died of gunshot wounds.
The BBC’s David Stern in Kiev says it is unclear what sparked the clashes, with protesters and police blaming each other.
The president is scheduled to meet protest leaders on Wednesday morning to discuss the constitutional proposals.
In a key development, one of Ukraine’s richest men – and a powerful financial backer of Mr Yanukovych – said on Tuesday that he believed there were “no circumstances that would justify the use of force against peaceful citizens”.
“Human losses and injuries suffered by protesters and law-enforcers during street clashes is an unacceptable price for political mistakes,” he said in a statement, calling for a return to negotiations for a peaceful solution to the crisis.
UN Secretary General Ban Ki-moon had earlier called for restraint and dialogue in Ukraine.
Several countries have also expressed concern at the sudden escalation of the crisis:
- The US National Security Council said it was “appalled by the violence” and urged President Yanukovych to “immediately de-escalate the situation and end the confrontation”.
- German Foreign Minister Frank-Walter Steinmeier called on both sides to “return urgently” to their attempts to find a political solution.
- The UK’s Minister for Europe, David Lidington, said such violence had “no place in a European democracy” and urged “all parties to return to the path of compromise and genuine negotiation”.
- Poland’s foreign ministry said it had summoned Ukraine’s deputy ambassador to express its concern, and called for “immediate dialogue”.