Arseniy Yatsenyuk said the opposition was generally ready to accept leadership, but several key demands must be met, including new elections.
Clashes continued overnight. Activists stormed a Kiev building housing police.
Viktor Yanukovych’s proposal came amid new efforts to end the deadly unrest.
He offered the post of prime minister to Arseniy Yatsenyuk and the position of deputy PM to former boxer Vitali Klitschko following talks on Saturday.
The opposition – confident in its position – appears to have taken these offers as a sign of weakness on Viktor Yanukovych’s part, and is forging ahead with the campaign to unseat him.
Speaking to large crowds in central of Kiev late on Saturday, the opposition leaders repeated their demands.
“Viktor Yanukovych announced that the government wasn’t ready to take the responsibility for the country and offered to the opposition to lead the government,” said Arseniy Yatsenyuk.
“What is our response to this? We are not afraid of the responsibility for the destiny of Ukraine.”
Later, Arseniy Yatsenyuk tweeted: “No deal @ua_yanukovych, we’re finishing what we started. The people decide our leaders, not you.”
Arseniy Yatsenyuk says that Tuesday, when a special session of parliament has been called, will be “judgement day”.
The opposition is demanding that a free trade agreement with the EU be signed and political prisoners be freed, including former PM Yulia Tymoshenko.
They are also demanding early presidential elections. A vote is not due until 2015.
Vitali Klitschko told the crowd that they would press ahead with their demands and that talks would continue: “We are not turning back and we will keep discussing and trying to find a direction.”
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