Opposition leaders have demanded the resignation of the government and early elections.
Yanukovych's presidential website reported his meeting with Commissioner for EU Enlargement Stefan Fule but gave no detail of what was discussed.
Boxer-turned-opposition leader Vitali Klitschko said outside mediation was needed if any progress is to be made in talks between the opposition and government.
"International mediators must be involved in any discussion of the crisis in Ukraine," he said.
"Yanukovych decided to declare war on his own people rather than stop the confrontation and approach resolving the situation with common sense. He tries to keep power at a price of blood and destabilize the country. He must be stopped."
Yanukovych and opposition leaders held a second round of talks Thursday, but they broke up without a resolution.
Both parties decided to keep talking, however.
Resolving the crisis, insists Klitschko, hinges on talks with the EU, especially with Fule.
"Yesterday minimal steps were proposed. They cannot solve the crisis. That is why such proposals outraged people. At first, they demanded Interior Minister Zaharchenko and (Prime Minister Mykola) Azarov's government to resign, but now the core demand is resignation of the President. But he pretends as if nothing is happening," Klitschko said.
In a Twitter post, the EU said foreign policy chief Catherine Ashton and a European Parliament delegation are also planning to travel to Ukraine next week.
Meanwhile, anti-government protesters worked Friday morning to strengthen barricades set up in central Kiev streets and seized a ministry building, Ukraine's official Ukrinform news agency reported.
Ukrainian Interior Minister Vitaliy Zakharchenko said early Friday that if protesters left the street where the violence has been focused, police would not seek to prosecute them.
He also promised police would not use force against those rallying in Kiev's Independence Square, or Maidan.
Police torture claims
Claims of abuses by security forces have emerged.
A video posted to YouTube, showing a protester made to strip naked apart from his shoes and kicked by police as he enters a van, has been widely circulated on Ukrainian media.
Ukraine's Interior Ministry has apologized for the behavior of those shown in the footage and says it is investigating the incident.
A 17-year-old who says he was taking pictures of the protests, Myhaylo Nyskohuz, told CNN he was tortured after he was seized by Ukraine's riot police, or Berkut.
"They beat me on my legs and ankles, they sprayed my whole body with pepper spray and made me lie naked and sing the national anthem," he said, looking battered and bruised.
"They stripped me and took me through a live corridor of around 40 or 50 riot police, and each one of them beat me."
Nyskohuz's arm was broken, and he was stabbed in the thigh.
Meanwhile, Yanukovych told a gathering of religious leaders that police were acting lawfully.
"Today, the law enforcement bodies are working within their power, within the laws that oblige them to keep order," he said.
He continued to call for the opposition to "sit down at the negotiating table."
He further said that anyone who had participated in rallies, but not committed a crime, would get amnesty.
"We agreed yesterday that after the parliament adopts the law on amnesty, all the people detained in the course of these actions, including the radical ones, but who haven't committed serious crimes, will be amnestied," the President said.
Prime minister: Officers told to act within the law
Prime Minister Mykola Azarov declined Thursday to apologize for the violence unfolding during the Kiev protests and told CNN's Richard Quest that law enforcement officers acted within the law.
Asked about Nyskohuz's case, Azarov replied:
"Well, first of all, the law enforcement officers were given instructions and orders to act within the legislation and not to use any kind of weapon.
"They do not have firearms with them, and those preliminary actions which they have to take -- when someone is trying, for example, to capture government buildings and institutions -- all those measures are not just analogical to those used in all the European states."
Police were merely responding to an effort to overthrow the government, Azarov said, adding that Ukraine was not in Russia's pocket.
Nyskohuz now faces a series of detention hearings to determine whether he will be jailed for taking part in the protests.
The Interior Ministry said Friday that 281 policemen have been injured since the violence erupted Sunday.
And as the protest movement spreads beyond the capital, 58 protesters were detained in Cherkasy, a city in central Ukraine, during an attempt to take over the regional state administration office, the ministry said.
'No to his resignation'
The protests flared into violence Sunday as protesters braved the freezing cold to voice their anger about sweeping new anti-protest laws approved by parliament last week.
Hundreds of protesters heard directly from Klitschko after the opposition talks with the President, which lasted more than four hours Thursday.
"He said no to his resignation and Cabinet resignation," Klitschko told opposition supporters.
"It does not make sense to negotiate with someone who intends to cheat."
The sharp rhetoric was echoed by the President's press office, which issued a statement after the talks.
"Unfortunately, for the second time, leaders of the opposition refused to declare the statement condemning extremist actions," it said.
The President's statement went on to say that "negotiations will be continued."
Sweeping anti-protest laws
The clashes are an escalation of weeks of largely peaceful public protests prompted by Yanukovych's decision in November to spurn a planned trade deal with the European Union and turn toward Russia instead.
The controversial protest laws have sparked concerns they could be used to put down demonstrations and deny people the right to free speech.
They include provisions barring people from wearing helmets and masks to rallies, from setting up tents or sound equipment without prior police permission, and from traveling in convoys of more than five vehicles without authorization.
The protests have unfolded since November 21, when Yanukovych changed his stance on the EU trade pact, which had been years in the making.
The demonstrators say an EU agreement would open borders to trade and set the stage for modernization and inclusion.
Ukraine's government says the terms needed to be renegotiated to protect Ukrainians better.