About 300 of the thousands of activists crowding the streets of Kiev gathered in front of the European Union delegation office in Kiev, chanting, "We need EU help" and "Sanctions," the Kiev Post reported.
Activist Dariya Kaleniuk, who works for the Anti-corruption Action Center, said other European countries have been quiet too long about the violence in Ukraine.
"Now, after yesterday's events it's time to freeze assets and impose real sanctions instead of talks," Kaleniuk said.
Confrontations between protesters and police in Kiev Sunday degenerated into street fighting, with protesters hurling pipes and cobblestones at riot squads that responded by using tear gas and a water cannon despite freezing temperatures.
Gazeta.ru, a Russian news portal, reported 70 police officers were wounded, 40 of them hospitalized. Dozens of protesters were reported injured.
Yaryna Yasynevych, another protester, told the Post if the European Union doesn't impose sanctions against Ukraine, it will "support dictatorship."
Yuri Lutsenko, one of the opposition leaders, told the New York Times protesters would revive a tactic they used in mid-December: blocking streets to government buildings to hamper the work of the Cabinet and administration.
"The siege of the government quarter will only intensify," Lutsenko said.
The Times said it was unclear whether a meeting between an aide to President Viktor Yanukovych and opposition leaders would take place as planned. Vitali Klitschko, the leader of the political party Punch said the opposition would only meet with Yanukovych, not the director of the national security council as suggested by the government.
Yanukovych met with Klitschko Sunday at his private mansion on the outskirts of Kiev.
"I told the president the situation needs urgent parliamentary and presidential elections. The president pretended he did not hear that," Klitschko later said in televised remarks.
"I don't rule out the possibility of civil war," he said, adding, "We must use every opportunity to resolve the crisis peacefully."
Protests began in November, after Yanukovych reversed field and declined to sign a sweeping free-trade agreement with the European Union, arguing it was bad for Ukraine. He later negotiated a package of financial aid from Russia.
They intensified against new laws enacted Thursday that stiffened the penalties for setting up tents and stages in public spaces. They banned wearing helmets and balaclavas, a tactic of the opposition activists to protect themselves against the police, identification or arrest. The new laws also clamp down on non-government organizations, similar to a Russian law that went into effect last year.
European Union foreign ministers and foreign relations chief Catherine Ashton were to discuss the situation Monday in at the bloc's headquarters in Brussels.
Ashton said she was following the events in the Ukraine "closely," EUobserver.com reported.
Ashton's envoy in Kiev, Jan Tombinski, posted on his Facebook page Sunday: "We call on people not to aggravate [an] already very difficult and dangerous situation. Attacking police may give reason to those who don't advocate [a] political solution of the crisis."
In a U.S. statement issued Sunday, the White House blamed the Ukrainian government for the violence and threatened sanctions.
"The increasing tension in Ukraine is a direct consequence of the government failing to acknowledge the legitimate grievances of its people," the statement said. "The U.S. will continue to consider additional steps -- including sanctions -- in response to the use of violence."