Nato foreign ministers have condemned the use of “excessive force” against pro-European protesters in Ukraine after a meeting in Brussels.
US Secretary of State John Kerry urged Ukraine to “listen to the voices of its people”.
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.
Thousands demonstrated outside the parliament building in Kiev on Tuesday, with protests in the city once again continuing into the evening.
“We urge all sides to conduct themselves peacefully. Violence has no place in a modern European state,” Mr Kerry told reporters.
The ministers said in a statement that they urged “Ukraine… to fully abide by its international commitments and to uphold the freedom of expression and assembly”.
“We urge the government and the opposition to engage in dialogue and launch a reform process,” they added.
Earlier on Tuesday, the Ukrainian parliament rejected an attempt to force the resignation of the government.
The opposition tabled the motion of no-confidence, which was defeated.
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.
Later he said the government was ready for dialogue with protesters but that they must “stop occupying government buildings and interfering with the work of the government administration”.
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.