The new attempt to uproot the protest stronghold came as President Viktor Yanukovych blamed opposition leaders for the worst violence in months of unrest.
After failed overnight talks, Viktor Yanukovych urged them to distance themselves from radical forces.
Activists say the violence has been stoked by the authorities.
Police launched their latest assault on Independence Square, also known as the Maidan, shortly after 04:00 local time. Several tents were set ablaze, and water cannon was later used.
Police had taken control of a corner of the square for the first time since December.
The clashes spread to surrounding streets and police launched a first attack on Independence Square on Tuesday evening.
In a statement, the health ministry said on Wednesday the number of dead on both sides had risen to 25. Nine of those killed were police, the interior ministry says. A journalist has also died.
Hundreds of people have been treated in hospital for injuries and there are fears the number of deaths could rise still further.
Explosions are taking place, fireworks are being thrown and large fires can been seen.
But the protesters appear to have been able to hold their defense lines, burning tires on the barricades.
Thousands of policemen have been surrounding the Maidan since Tuesday, although reports suggest that many anti-government activists are heading to join the camp.
President Viktor Yanukovych said in statement on Wednesday morning: “The opposition leaders have disregarded the principle of democracy according to which one obtains power not on the streets or maidans – but through elections.”
“They have crossed the line by calling for people to take up arms,” he said, warning that those responsible for violence would face the law.
The president added that there was a “better and more effective way” to solve the crisis – through dialogue and compromise.
“It is not too late to stop the conflict,” Viktor Yanukovych said.
Security forces had given the protesters a deadline of 18:00 on Tuesday to leave the square, the scene of a mostly peaceful protest camp since November.
When the deadline expired, riot police advanced with an armored vehicle, dismantling barricades and firing stun grenades and water cannon.
Protesters have been resisting, throwing missiles from behind piles of burning tires.
In speeches from the main stage through the night, 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 Vitaly Klitschko, the leader of the Udar (Punch) party.
Arseniy Yatsenyuk, who heads the Fatherland party, appealed to President Viktor Yanukovych to “stop the bloodshed and call a truce”.
Earlier on Tuesday, police blocked protesters from marching on parliament, where lawmakers had been due to debate proposed changes to the constitution.
The debate did not take place. Arseniy Yatsenyuk said President Viktor Yanukovych was blocking the reforms and that his allies “show no desire whatsoever to end the political crisis”.
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