The opposition, led by presidential contender Viktor Yushchenko, claims the government helped rig the election in favour of his rival, Moscow-leaning Prime Minister Viktor Yanukovich, and has asked the court to order either a recount or a fresh ballot.
The Supreme Court, which operates independently from the government, has the power to annul the elections.
Tens of thousands of demonstrators are expected to gather around the court building after Mr Yushchenko’s main supporter, opposition lawmaker Yulia Timoshenko, called on them to “not put pressure on it, but support honest judges”.
The opposition has said it will ask for international mediators to intervene if its call is not accepted by Monday.
Ukraine’s Yanukovich bastions in the southeast have warned they would declare greater autonomy if their candidate fails to become president, fanning fears that the crisis could split the former Soviet republic.
Mr Yanukovich met some 3,500 local officials from 17 of Ukraine’s 27 regions — which make up two-thirds of the country’s population — and warned the country is heading toward an imminent collapse.
He denounced a vote in parliament on Saturday which declared the November 21 poll invalid.
After a heated meeting in the eastern region of Lugansk, local leaders said in a joint statement they would hold a referendum on the “possible change in the administrative and territorial status of Ukraine” – should Mr Yushchenko come to power.
The strategic coal mining region of Donetsk became the first to set an autonomy vote by scheduling a December 15 referendum on whether to proclaim itself a “republic.”
Meanwhile in Kiev, tens of thousands of opposition protestors streamed into central Independence Square, which has turned into a week-long political demonstration in support of Mr Yushchenko.
The opposition leader told his followers that the Russian-speaking regions allied with Moscow had to be punished for threatening to break off.
“We demand the opening of a criminal inquiry against the separatist governors,” he said.
The stand-off over the presidential vote has exacerbated tensions between Ukraine’s west — nationalist, Ukrainian-speaking and once part of Poland with a large Uniate Catholic population — and its east — industrialised, Russian-speaking, mostly Orthodox and with strong cultural ties to Russia.
Western observers have claimed the election was marred by widespread fraud and Washington and the European Union have urged Ukraine’s authorities to “review” the official vote results.