Ukrainian opposition leader Arseniy Yatsenyuk says protests will continue despite President Viktor Yanukovych's offer to appoint him as prime minister.
Mr Yatsenyuk said the opposition was generally ready to accept leadership, but several key demands must be met, including new elections.
Meanwhile clashes have continued in Kiev, with activists trying to storm a building where riot police are based.
The president's proposal came amid new efforts to end the deadly unrest. He offered the post of prime minister to Mr Yatsenyuk and the position of deputy prime minister to former boxer Vitali Klitschko following talks on Saturday.
Mr Yatsenyuk is an ally of the jailed ex-Prime Minister Yulia Tymoshenko and parliamentary leader of the country's second biggest party, Fatherland.
Speaking to large crowds in central of Kiev late on Saturday, the BBC reports that opposition leaders did not explicitly say whether they accepted the offer but repeated their demands.
The opposition is demanding that a free trade agreement with the European Union be signed and political prisoners be freed, including former Prime Minister Yulia Tymoshenko.
They are also demanding early presidential elections. A vote is not due until 2015.
Protests began in November after Ukraine decided not to sign an accord on more co-operation with the European Union. Instead, the government opted to deepen ties with neighbouring Russia.
The crisis escalated this week when two activists were killed, and another was found dead with torture marks in a forest near the capital.
A fourth, a 45-year-old protester is said to have died in a Kiev hospital on Saturday, after sustaining injuries in earlier violence.