Clashes with police broke out a week ago in the wake of new, harsh anti-protest laws.
More-moderate opposition figures, including heavyweight boxing champion Vitali Klitschko, have tried appealing to stop the clashes, but have been booed, and one time Klitschko was sprayed with a fire-extinguisher.
Another top opposition figure, Arseniy Yatsenyuk, said Saturday that the protests will continue despite the offer by embattled President Viktor Yanukovych to make him prime minister.
The protests began in Kiev after Yanukovych shelved a long-awaited trade pact with the European Union in favor of securing a bailout loan from Russia, and boiled over into violence a week ago over the new anti-protest laws.
Yatsenyuk told the crowd at the main protest site that Yanukovych must still meet several key demands of the opposition and that talks will continue.
Yatsenyuk said a special session of parliament called for Tuesday could be decisive. Yanukovych has said that session could discuss a government reshuffle and changes to the new anti-protest laws.
Those laws ignited clashes between police and protesters a week ago at a site near the Ukrainian parliament, about a 10-minute walk from Independence Square.
The building under attack on Sunday lies between those two points. The assault started after an estimated 200 police were seen entering the building and speculation spread that they were preparing to disperse demonstrators.
"Tuesday is judgment day," Yatsenyuk told protesters, referring to the parliament session. "We do not believe a single word of theirs. We believe only actions and results."
At a later news conference, Yatsenyuk said, "We are not throwing out the proposal, but we are not accepting it, either. We are conducting serious consultations among three opposition forces."
He also said the opposition would demand that the government sign a free trade agreement with the EU and release political prisoners, including former Prime Minister Yulia Tymoshenko.
The opposition also is demanding early presidential elections.
Yanukovych's latest offer, coming as protester anger rises and spreads from the capital to a wide swath of the country, appeared to have been both a concession and an adroit strategy to put the opposition in a bind.
Accepting the offer could have tarred Yatsenyuk among protesters as a sell-out, but rejecting it would make him appear obdurate and unwilling to seek a way out of the crisis short of getting everything the opposition wants.
The offer came hours after the head of the country's police, widely despised by the opposition, claimed protesters had seized and tortured two policemen before releasing them. The opposition denied it and said Interior Minister Vitali Zakharchenko was making a bogus claim in order to justify a police sweep against protesters.