But Yanukovich denounced the prime minister's accusation as a "pure, arrogant lie".
"How can the opposition falsify results? Only the authorities have that ability - they have the mechanism, structure, the interior ministry," he said.
Tymoshenko has called for the Organisation for Security and Co-operation in Europe, to ensure the January 17 election is fair, Russia's Interfax news agency reported.
The row comes a day after Viktor Yushchenko, the Ukrainian president who is also running for re-election, said victory for either Tymoshenko or Yanukovich "will return us to the swamp for decades".
Yushchenko became president in an unprecedented third round of voting in 2004, after mass protests against electoral fraud led to victory being denied to the Moscow-backed Yanukovich.
But according to recent opinion polls, Yushchenko has little chance of being re-elected.
Analysts have also remained doubtful that Ukraine is likely to see a repeat of the mass rallies of the Orange Revolution that swept Yushchenko and Tymoshenko to power.
A Ukrainian court has banned all mass rallies on Kiev's Independence Square, the heart of the 2004 protests, for the next three weeks, local media reported.
Yanukovich and Tymoshenko are expected to face each other again in a February 7 run-off vote.