World boxing champion Vitali Klitschko, nationalist leader Oleg Tyagnybok and the head of the party of jailed opposition leader Yulia Tymoshenko, Arseniy Yatsenyuk, were all in attendance.
Yanukovych promised an amnesty for those arrested during the protests and said he would consider sacking officials responsible for working on the Association Agreement.
The opposition however said it was not enough, insisting that the government of Prime Minister Mykola Azarov should resign.
The opposition is planning a new mass protest on Sunday.
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The talks came after Ukraine's richest man and hugely influential powerbroker Rinat Akhmetov called on all parties to find a peaceful solution to Ukraine's deepest political crisis in a decade.
The "round table" talks are chaired by post-Soviet Ukraine's first president Leonid Kravchuk.
"I am ready to find a path that would give hope to the Ukrainian people that we are capable of overcoming such crises," Yanukovych said.
Akhmetov -- who according to the Ukrainian edition of Forbes magazine is the country's richest man with a $14.9 billion fortune -- said it was important now to have a "balanced approach" and for all sides to sit down for negotiations.
"Politicians, government officials, the opposition, and moral leaders of the country must sit down at the negotiating table and make a decision we will be proud of," he said in a statement earlier today.
He can either sign a deal with the European Union that would put his ex-Soviet nation on track to eventually joining the bloc, or join a Moscow-led Customs Union, which Russia sees as a future alternative to the EU.