Ukrainian opposition leader and boxing champion Vitali Klitschko has said that he wants presidential elections this year.
He said the opposition would not yield in its demands.
"Our demand is the holding of presidential elections this year... We will not yield but talks will continue," he told protesters after President Viktor Yanukovych offered the opposition the post of prime minister to end the country's crisis.
The presidential website said after the two sides met for talks aimed at seeking an end to a violent political crisis.
Former economy minister Arseny Yatsenyuk would be offered the post of prime minister.
Vitaly Klitschko, an internationally known boxer, would be proposed as deputy prime minister responsible for humanitarian issues, the website said.
If Mr Yatsenyuk accepts the post of prime minister the president would be ready to accept the resignation of the government of Mykola Azarov, the website said.
Earlier, anti-government protesters in the Ukrainian capital Kiev have started a large fire just a few hundreds metres away from the main government building.
Masked men and a few women, many wearing helmets and protective clothing hurled Molotov cocktails and tyres into a burning flame in front of a barricade that was enforced the night before.
The sound of drums and metal bars could be heard over the square and neighbouring streets for hours.
Kiev residents brought hundreds of old car tyres to feed the fire and used human chains to pass them along.
Many of the protesters have spent days in the city centre, which is partly controlled by the opposition.
In the past couple of days, protesters have built new barricades using snow and metal bars.
Riot police did not not try to storm the makeshift fortifications, but used sound bombs and water from fire engines to douse the fire.