Explosions are taking place, fireworks are being thrown and large fires have broken out in Independence Square, known locally as the Maidan.
On Tuesday at least 21 people were killed, including seven policemen, in the worst violence seen in weeks.
Opposition leaders later met President Viktor Yanukovych but failed to find a solution to the crisis.
Vitaly Klitschko, leader of the opposition Udar (Punch) party, told Ukraine's Hromadske TV that the president had given the protesters only one option, leave the Maidan and go home.
Meanwhile, Mr Yanukovych's aide said the president was preparing to address the nation, without providing further details.
'Island of freedom'
Security forces had given protesters a deadline of 18:00 local time (16:00 GMT) to leave Independence Square, the scene of a mostly peaceful protest camp since November.
The city's metro service was completely shut down, and there were reports that cars were being prevented from coming in to the capital.
Then shortly before 18:00 GMT, police announced over loudspeakers that they were about to begin "an anti-terror operation".
At the scene
Exactly a month ago, the nation was shocked by the deaths of protesters during clashes with riot police in central Kiev.
On Tuesday Ukrainians again saw dead bodies strewn on the city streets, dozens of injured people.
Despite the shock, many came to the main protest camp, the Maidan, to support activists trained to defend barricades from the riot police.
Crowds grew as streams of people, including women, headed to the Maidan.
Many had to walk as Kiev's metro was completely shut down for the first time since Ukraine gained independence in 1991.
The authorities said they had closed the metro because of the danger of "terror acts" in the capital.
They advanced with an armoured vehicle, dismantling barricades and firing stun grenades and water cannon.
Protesters threw fireworks and petrol bombs, and lit fires to block off police.
Many tents have been burned but it was unclear whether there had been casualties.
Late on Tuesday, the police tried to break through a barricade from the Evropeyska Square, but the attack was repelled.
In a renewed assault shortly after 04:00 local time on Wednesday (02:00 GMT), the police tried to move on the protesters' tents near the main monument on the square.
A number of tents were set ablaze, and the police reportedly again began using water cannon.
In speeches from the main stage, protest leaders urged people already on the Maidan to stand firm, and called on Ukrainians elsewhere to come to the square.
"This is an island of freedom and we will defend it," said Mr Klitschko.
Arseniy Yatsenyuk, who heads the Fatherland party, appealed to President Yanukovych to "stop the bloodshed and call a truce".
"We are talking about human lives and the future of the country which could be drowned in blood. Stop, Viktor Yanukovych, stop," he said.
Meanwhile, there are reports of unrest breaking out elsewhere in Ukraine, including the western cities of Lviv, Ivano-Frankivsk.
The BBC's David Stern in Kiev says this is a key moment for the country and that many people are scared of further escalation.
Although this does not necessarily mean a civil war - as some have previously suggested - Ukraine remains dangerously divided, our correspondent says.
Ukraine's unrest began in November, when President Yanukovych rejected a trade deal with the EU in favour of closer ties with Russia.
Pro-EU protesters demanded his resignation and snap elections. After weeks of unrest, the mood had calmed in recent days, but people remained on the streets.
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.
Police fired stun and smoke grenades, and rubber bullets.
Correspondents say it was unclear what sparked the latest violence, with each side blaming the other.
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.
Police said late on Tuesday that at least 21 people had been killed, including seven police officers.
The White House said it was "appalled" by the violence, saying "force will not resolve the crisis".
Spokesman Jay Carney urged President Yanukovych to "restart a dialogue with opposition leaders today".
UN Secretary General Ban Ki-moon had earlier called for restraint and dialogue.
In other international messages of concern:
German Foreign Minister Frank-Walter Steinmeier said Ukraine was "experiencing dramatic hours" and that the EU could consider imposing sanctions.
The UK's Minister for Europe, David Lidington, said such violence had "no place in a European democracy".
EU foreign policy chief Catherine Ashton earlier said she was "deeply worried" about the unrest and urged politicians to "address the root causes".
Russia blamed the earlier violence on "connivance by Western politicians" and their refusal to consider the "aggressive actions" of radical factions within the protest movement.
Rinat Akhmetov, one of Ukraine's richest men - and a powerful financial backer of Mr Yanukovych - said there were "no circumstances that would justify the use of force against peaceful citizens".
Source: BBC News