Officials in eastern Ukraine say they will split their region from the rest of the country if opposition leader Viktor Yushchenko becomes president.
Yushchenko supporters are on the streets again
After meeting in the power base of Prime Minister Viktor Yanukovych, governors vowed to hold a referendum if Mr Yanukovych's win was overturned.
Mr Yushchenko has already warned that this threatens the future of Ukraine.
Outgoing President Leonid Kuchma has urged both sides of the dispute to work to find a compromise.
The Russian government has suggested it might reverse its opposition to a new election. The European Union has already called for a new vote.
Ukraine's supreme court is due to meet on Monday to consider the validity of last Sunday's run-off poll, which saw pro-Russian Mr Yanukovych declared the winner.
Pro-Western Mr Yushchenko has claimed victory in the election, alleging massive fraud. His concerns have been backed by international observers.
Mr Yanukovych met about 3,500 local officials from 17 of Ukraine's 25 regions in the eastern city of Severodonetsk.
He told delegates the disputed presidential election had pushed Ukraine to the "brink of catastrophe".
He said: "There is one step to the edge. When the first drop of blood is spilled, we will not be able to stop it."
Later, he looked on as delegates voted for "a referendum to be held in December this year to determine the region's status" and said he did not support the move.
Tens of thousands of protesting supporters of pro-Western Mr Yushchenko remain on the streets of the capital, Kiev.
POLITICAL CRISIS TIMELINE
21 Nov: Viktor Yanukovych declared winner of run-off poll
Independent observers declare the elections flawed, and thousands take to the streets
25 Nov: Supreme court suspends publication of result until it considers the opposition's complaints
26 Nov: Mr Yanukovych and Mr Yushchenko hold talks and agree to seek peaceful solution
27 Nov: MPs declare election invalid, pass vote of no-confidence in the election commission
28 Nov: Eastern regions threaten to secede if Mr Yushchenko is declared president
Addressing them earlier, Mr Yushchenko said "those people who will raise the issue of separatism will be held criminally responsible under the Ukrainian constitution".
President Kuchma said working group talks between representatives of the two rivals, designed to end the crisis, were going badly.
In a televised statement on Sunday, he accused Mr Yushchenko of not showing "goodwill", calling on him to lift a blockade by his supporters of government offices.
"No-one can say what sort of compromise can be found or whether one will be found at all," said Mr Kuchma.
The Severodonetsk decision is clearly meant to be a threat - a way of putting pressure on talks taking place between the two sides, says the BBC's Jonathan Charles.
The working groups were set up following talks on Friday with EU and Russian mediators.
According to the official election result, Mr Yanukovych won with 49.46% of the vote against Mr Yushchenko's 46.61%.
The supreme court suspended the presidential poll result on Thursday to consider the opposition's complaints.
In a non-binding resolution on Saturday, Ukraine's parliament declared the poll invalid, saying the result was "at odds with the will of the people".