Explosions are taking place, fireworks are being thrown and large fires have broken out in Independence Square.
On Tuesday at least 18 people were killed, including seven policemen, in the worst violence seen in weeks.
President Viktor Yanukovych blamed the violence on opposition leaders, but said it was still “not too late to stop the conflict”.
He was speaking after a late-night meeting with opposition figures Vitaly Klitschko and Arseniy Yatsenyuk.
‘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”.
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.
Mr Yatsenyuk, who heads the Fatherland party, appealed to President Yanukovych to “stop the bloodshed and call a truce”.
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. – Full Read – BBC: Ukraine crisis: Police storm main Kiev ‘Maidan’ protest camp