Yanukovych met with Arseniy Yatseniuk, head of the Batkivschyna party, UDAR party leader Vitali Klitschko, and Oleh Tiahnybok, leader of the Svoboda party, as well as Justice Minister Olena Lukash, Andriy Kliuyev, the head of president's administration and head of the working group, and presidential advisor Andriy Portnov, Interfax, Ukraine, reported.
Following the meeting, Yanukovych offered the post of prime minister to Yatseniuk and the role of deputy prime minister for humanitarian affairs to Klitschko, Lukash said.
"To launch a wide-scale public dialogue, the Ukrainian president challenged Vitali Klitschko to meet him in a public debate. Klitschko agreed," Lukash said.
Meanwhile, opposition leaders urged pro-Western protesters in Kiev to remain peaceful, CNN reported.
"We call on all Ukrainian citizens not to succumb to provocations of authorities and continue the protest exclusively in a peaceful manner," said a statement from the UDAR party.
Ukraine Interior Minister Vitaliy Zakharchenko Saturday accused protesters of attacking police with gasoline bombs and killing one officer with a firearm.
He said he's concerned with the stockpiling of firearms at government buildings in Kiev.
"The recent events in Ukraine showed that our attempts to settle the conflict by not using force have been in vain. Our appeals haven't been heard, the agreements for truces are violated ... According to information received by law enforcers, firearms being piled up at House of Trade Unions and Kiev City State Administration," he said in a statement quoted by Interfax-Ukraine.
He said protesters were using gasoline bombs against police and accused Radical Party leader Oleh Liashko of calling for attacks on police.
"During the night one policeman was shot dead, and three policemen were captured on Independence Square. One of them is in hospital with a serious injury, and two still are being held in the building of Kiev City State Administration," Zakharchenko said.
Protesters in Ukraine armed with clubs said they seized the country's Fuel and Energy Ministry building in downtown Kiev Saturday, though ministry officials said otherwise.
"The guards did not put up a fight. We will continue our work to paralyze the central bodies of government," Alexander Danilyuk, a leader of the opposition group Common Cause, said.
Fuel and Energy Minister Eduard Stavitsky released a statement saying "the ministry is functioning as normal."
The possible building seizure came one day after thousands of protesters gathered in Kiev and seized the Agrarian Policy and Food Ministry building, RIA Novosti reported.
A surge of violent demonstrations began last week after the Ukrainian government enacted laws restricting protests. Since the demonstrations began, authorities said two protesters were killed, though opposition leaders said at least five have died.