The Ukrainian parliament has rejected an attempt to force the resignation of the government.
The opposition tabled the motion of no-confidence, which was defeated, as thousands of demonstrators protested outside the parliament building.
Earlier, Prime Minister Mykola Azarov apologised in parliament for the use of police force against protesters.
Mass protests were sparked by the government's decision not to sign an association deal with the EU last week.
The motion of no-confidence in Mr Azarov's government was supported by 186 members of the main opposition parties, but fell short of the 226 votes required for approval.
Before parliament voted on the motion, Mr Azarov addressed an emergency session:
"On behalf of our government, I would like to apologise for the actions of our law enforcement authorities on Maidan [Independence Square]," he said, referring to violence at the weekend. "The president and the government deeply regret that this happened."
Speaking above boos by opposition deputies in parliament, the prime minister called for protests outside the government buildings in Kiev to end, and appealed for Ukrainians not to return to the unrest of the Orange Revolution of 2004.
"We reach out our hand to you. Push away the plotters, the plotters seeking power and who are trying to repeat the scenario of 2004," he said.
On Monday, Mr Azarov had said he saw "all the signs of a coup" as protests intensified.
He said the government was aware of plans to seize the parliament building.
Demonstrators are demanding the resignation of Mr Azarov and President Viktor Yanukovych, and have called for a general strike.
Mr Yanukovych - who has gone ahead with a planned visit to China - has warned that the rallies should only be peaceful after violence at the weekend.
The main opposition leaders have condemned the violence, saying it was the work of "provocateurs".
The newspaper Ukrainska Pravda published a series of videos and photographs which it says backs up the claims.
The images appear to show a group of young men wearing masks and helmets pushing against police lines in front of the presidential building. Soon afterwards several are seen beckoning to others in the crowd and then passing through the blockade, without resistance from officers.
At least one of the men is also pictured standing uninterrupted behind the riot police.
In another development, on Monday Mr Yanukovych asked the European Commission to allow him to send a delegation for talks on "some aspects" of the EU association agreement that Ukraine had been expected to sign, officials in Brussels said.
Commission President Jose Manuel Barroso agreed to the request, but stressed the Commission was ready to discuss implementation of accords already initialled, "but not to reopen any kind of negotiations".
Opposition leaders have renewed demands that Mr Yanukovych stand down, and urged him to "stop political repression".
The protests began just over a week ago after a halt was ordered to preparations to sign a deal on closer integration with the EU.
'Out with the gang!'
Hundreds of people put up tents on Independence Square on Sunday night, after a mass rally that drew hundreds of thousands, amid calls for a general strike.
The headquarters of the cabinet has been blockaded, with government employees unable to reach work.
Police reinforcements are being sent to Kiev, Ukrainska Pravda reported.
As thousands of protesters converged on Independence Square on Monday, they chanted slogans including "Out with the gang!"
Prime Minister Azarov, quoted by Interfax news agency, said the political opposition in Ukraine had the "illusion" that it could overthrow the existing order.
"We know that a plan is being prepared to seize the parliament," he said.
Speaking during a meeting, Mr Azarov told Western ambassadors on Monday: "This has all the signs of a coup...
"That is very serious. We are patient, but we want our partners not to feel that everything is permitted."
Later on Monday, the US weighed in to dispute Mr Azarov's interpretation.
"We certainly don't consider peaceful demonstrations coup attempts," a White House spokesman said.
Jay Carney added that while violence by the authorities against demonstrators on Saturday had been "unacceptable", the police had in general been more restrained since.
For his part, President Yanukovych urged police and demonstrators to observe the law.
"Any bad peace is better than a good war," Mr Yanukovych said in a TV interview reported by his own website - his first comments on Sunday's violence.
President Vladimir Putin of neighbouring Russia said events in Ukraine seemed "more like a rampage than a revolution."
Mr Putin blamed "outside actors" for the protests, which he said were an attempt to unsettle Ukraine's "legitimate" rulers.
On Sunday, several hundred thousand people took part in a march, defying a ban on rallies.
There were clashes near the presidential building, with demonstrators firing flares and riot police using tear gas, batons and stun grenades. TV footage appeared to show officers beating reporters.
There were also clashes on Sunday as Kiev protesters tried to topple a statue of Lenin.