"If we really want to preserve peace ... let us have new elections," the BBC quoted Kuchma as saying, adding the country needed "a legal president."
Official results released by Ukraine's Central Election Commission said 96.65 percent of registered voters cast ballots in last week's election, which many independent and western observers condemned as flawed.
Liberal opposition leader Viktor Yushchenko wants the Nov. 21 victory of rival Prime Minister Viktor Yanukovych nullified due to the fraud claims and a new vote held Dec. 12.
Yanukovych Monday he would accept new elections in the contested regions of Donetsk and Luhansk -- if the fraud claims were proven.
Thousands of demonstrators on both sides of the issue were outside the high court Monday as the 22 judges began investigating the charges.