After a violent night when protesters besieged a building where police were sheltering, Ukraine's capital is preparing for a large demonstration that will test the opposition's determination and authorities' patience.

Throughout Ukraine's two-month-long political crisis, Sunday rallies have typically attracted crowds of tens of thousands and sometimes much larger.

The latest rally comes a day after beleaguered President Viktor Yanukovych offered the country's prime minister post to one of the opposition's top leaders. While not rejecting the offer outright, Arseniy Yatsenyuk said more of the opposition's demands must be met, including Yanukovych's resignation. He vowed protests will continue.

Late Saturday, demonstrators threw firebombs and rocks into a building in central Kiev where about 200 police were sheltering. After several hours, the crowd formed a corridor and allowed police to leave.