But Zourabichvili, who has alleged repeatedly that the vote count was falsified to give victory to her opponents in the ruling Georgian Dream party, said it was not her job to supply the evidence.
"It's not up to the president to provide proof of election fraud," she told reporters on Wednesday.
"Observers and everyday citizens have shown proofs of how massive the rigging of elections was."
Zourabichvili and other government critics have cast the vote as a pivotal moment for Georgia, a country which has ambitions to join the European Union but which the West sees as drifting back into Russia's orbit under the leadership of Georgian Dream.
The president's apparent refusal to cooperate with the investigation raises legal and constitutional questions in a country with a volatile post-Soviet history including war, revolution and mass protests.
Ukrainian President Volodymyr Zelenskiy said the West should admit Russia has "won" in Georgia and was on its way to doing the same in Moldova unless Western rhetoric against crossing Moscow's red lines was dropped.
"We have to recognise in Georgia for today Russia won. First, they took part of Georgia, then they changed policy, the government. And now (Georgia) has a pro-Russian government," Zelenskiy said in English in a video released on Wednesday.
Another former Soviet republic, Ukraine's neighbour Moldova, will hold a presidential election runoff on Sunday after pro-European incumbent failed to secure more than 50 per cent of the vote.
Huge crowds demonstrated earlier this year against a "foreign agent" law that Georgian Dream pushed through parliament, and thousands took part in a rally to protest against the weekend election result.
"I just want to say that my answer to the prosecutor's request that I present proofs to sustain my declarations on the results of the elections is not relevant because the prosecutor should be doing its own investigation," Zourabichvili said.
"That's what the prosecutor's office is there for."
Election observers, including the 57-nation Organisation for Security and Co-operation in Europe (OSCE) have said that the vote was marked by incidents of voter intimidation, bribery and ballot-stuffing that could have impacted the result, but stopped short of calling it rigged.
Official results gave Georgian Dream 54 per cent of the vote and a clear majority in parliament. Opposition politicians have said they will boycott the chamber in protest.
Georgian Dream says it wants the South Caucasus country to one day join the EU but will not let it be dragged into another conflict with Moscow, which won a short war against it in 2008.
Zourabichvili told Reuters on Monday that Georgian Dream had used a Russian "methodology" to falsify the election result, citing two exit polls which had pointed to an opposition victory.
The Kremlin has denied interference allegations and accused the West of trying to unduly influence the outcome of the vote.
