Election results were due to be published by state media on Thursday, officially validating the vote.
But Zoya Sharikova, a spokeswoman for the Communists, said her party was seeking to contest the election results due to alleged violations concerning voting abroad.
The party's allegation comes after Al Jazeera learned that election monitors accused officials of rigging the elections before last month's vote
Monitors said more than 10,000 blank ballot papers, due to be destroyed, were apparently put into ballot boxes.
The decision could lead to further delays in establishing a new government in the ex-Soviet republic.
Yushchenko and Tymoshenko's parties won 228 seats in the 450-member Verkhovna Rada, or parliament, which was two seats more than a bare majority.
|Blank ballot papers, due to be destroyed, were |
apparently put into ballot boxes.
The rival Party of Regions, led by their main opponent, and more Moscow-friendly Viktor Yanukovych, the prime minister, won more votes than any other party but only 175 seats.
An informal agreement concluded by the Tymoshenko bloc and Yushchenko's Our Ukraine/People's Self-Defence party earlier this week stipulated that Tymoshenko would be prime minister while Yushchenko's bloc would pick the parliament speaker.
A majority coalition can be officially formed once parliament convenes. The legislature has about one month to convene after the official publication of the election results.
Tymoshenko's return to the premiership would resurrect an alliance first formed during the so-called Orange Revolution of 2004 that saw Yushchenko win the presidency in a re-run election.
Yushchenko and Tymoshenko have campaigned on promises to foster closer relations with the EU, fight corruption reform and raise standards of living.