The Ukrainian Interior Ministry released a statement saying police had been trying to secure the streets to enable city business to resume and had no plans to clear the square.
Police did make deep inroads into the protest area during the night, but in some cases they spent hours dismantling barricades erected over the past two weeks.
Where they met protesters, they pushed with their shields for the most part rather than wading in swinging clubs. There were reports of several dozen injuries.
After the police withdrew, protesters immediately reoccupied the streets that had been cleared. Many expect the police to come back as darkness falls, but for the moment the action appeared to stir a great deal of emotion while seemingly accomplishing little.
The action came hours after foreign envoys and three former presidents urged a peaceful solution to the dispute.
The protest began after President Viktor Yanukovych decided not to sign a trade agreement with the European Union and turned toward Russia instead. Its numbers grew considerably after police beat demonstrators on the night of Nov. 30, and it became a general protest against the government.
On Sunday, hundreds of thousands of demonstrators turned out to express their anger at Yanukovych. Neither side showed any interest in backing down.
Yanukovych said Tuesday on national television that he wanted to meet with opposition leaders, but he added that the continuing encampment was unacceptable.
Both Catherine Ashton, the foreign policy chief of the European Union, and Victoria Nuland, a U.S. assistant secretary of state, were in Kiev on Tuesday urging a peaceful resolution. Appearing with Yanukovych on TV were former Ukrainian presidents Leonid Kravchuk, Leonid Kuchma and Viktor Yushchenko, all of whom also said the only way to end the conflict was through negotiation.
Nearly an hour after the police action began about 1:30 a.m., protesters still held a stage in the middle of the square. The police were methodically dismantling barricades.
It was unclear what had happened to the occupied City Hall several hundred yards down the street called Khreshatyk, or to a building belonging to the trade union federation that had become a sort of headquarters for the protesters.
Heavyweight boxing champion Vitali Klitschko, an opposition politician and head of the UDAR party, had warned Yanukovych that a police assault would leave blood on the president’s hands.
Oleksandr Shevchenko, from the town of Bila Tserkva, was typical of many protesters interviewed Tuesday in saying he did not believe the government would dare launch an assault against such a large number of people in a dispute that has attracted so much attention.
The bells of the Mikhailovsky Cathedral, up a hill to the north of Independence Square, rang out after the police began storming the square, apparently as an alert to the residents of the neighborhood.
Yanukovych was the biggest loser of the 2004 Orange Revolution, when a similar large gathering formed after he was declared the winner of rigged elections. Eventually, after a roundtable set of negotiations, the elections were held over and he lost to Yushchenko. He finally won the presidency in an election in 2010, and immediately began prosecuting his main political rivals, chief among them the former prime minister, Yulia Tymoshenko.