The most important power base of President Milosevic is now under serious threat after the far-right Radical party, which rules Serbia in coalition with the Milosevic regime, offered its support to the opposition.
It emerged yesterday that the Radical leader, Mr Vojislav Seselj, contacted the opposition directly and offered his help. The move opens up a real possibility of overthrowing Mr Milosevic's hold on his legislative power base within the Serbian republic government by the end of this year.
The Radicals are the most strident force in Yugoslav politics and their support for the Democratic Opposition of Serbia (DOS) marks a major political shift.
Mr Seselj is a former paramilitary, active during the war in Bosnia. He is famous in Belgrade for waving a gun on the streets on more than one occasion. Most recently, he threatened local journalists, saying they should be "liquidated".
The Radicals are in the republican government of Serbia with the Socialist party of President Milosevic and the Yugoslav Left party of his wife, Mrs Mira Markovic.
Mr Seselj and his party have the power to provoke a crisis in the republic's government - but it may be that they will decide to stay in government and to work against Mr Milosevic from within. "It's easy to bring down a government, but we are not in a hurry," Mr Seselj said yesterday.
Opposition leaders piled the pressure on President Milosevic to step down yesterday, calling for a mass campaign of civil disobedience as tens of thousands of opposition supporters rallied across Serbia.
Up to 20,000 people gathered in Belgrade's central Republic Square for a second protest yesterday, as police maintained a low-key presence, with no incidents reported during the two-hour gathering.
In the southern Serbian city of Nis, an estimated 35,000 people rallied, demanding that Yugoslav authorities recognise Mr Kostunica as the outright winner of Sunday's election.
In Novi Sad, Serbia's second-largest city, more than 15,000 people flooded the streets. Opposition leaders said they would stage new protests today.
The opposition also unveiled a national campaign of civil disobedience yesterday. DOS official Mr Zoran Djindjic said "the whole of Serbia will stop on Monday" if Mr Kostunica's presidential win was not recognised.