Members of Ukraine Prime Minister Yulia Tymoshenko's bloc say they will contest in court the conduct of the presidential vote after her apparent defeat.
An official says the bloc will contest results in some areas and seek recounts while another is reportedly accusing opposition leader Viktor Yanukovych's party of falsification.
Mrs Tymoshenko has not spoken in public but reportedly told allies she would never accept Mr Yanukovych's win.
The BBC reports she scheduled news conferences in Kiev twice on Monday, but then cancelled them.
However, foreign monitors have said the election on Sunday was free and fair.
With 99.94% of votes counted, Mr Yanukovych had 48.94% to 45.48% for Mrs Tymoshenko.
Full election results are expected later on Tuesday, according to the Russian Interfax news agency.