Kiev authorities said Friday they have received a permit application from supporters of opposition leader Viktor Yanukovych for a rally of up to 50,000 people the day after the vote.
Prime Minister Yulia Tymoshenko has threatened a rerun of the 2004 Orange Revolution, when hundreds of thousands of demonstrators protested a rigged election.
Each has accused the other of planning to steal the election.
President Viktor Yushchenko on Friday instructed police to secure the Central Election Commission, surrounded by some 250 burly Yanukovych partisans.
It was not clear if police would evict the demonstrators. The protest leader said they were there to make certain Tymoshenko supporters don't hijack the vote.
Acting Interior Minister Yury Lutsenko, an ally of Tymoshenko, said the massing of so many security veterans raises concerns about election unrest. Yanukovych's spokesman declined to comment on Lutsenko's statement.