His call came after opposition candidate Viktor Yuschenko declared himself the winner of weekend elections, which he charges were rigged by massive vote fraud.
The talks -- to discuss the allegations that election fraud was responsible for the narrow win of Prime Minister Viktor Yanukovych -- are expected to take place this morning.
Ukraine's Central Election Commission says it will announce the final results later today.
The Interfax news agency quotes election officials as saying the commission plans to make the announcement after a meeting in Kyiv.
Kuchma criticized the declaration by Yuschenko in a mock ceremony yesterday that he had won the election, calling it a "political farce" that could have dangerous consequences.
Official results say Yanukovych received 49.39 percent of the vote, and Yuschenko 46.71 percent, with 99.48 percent of votes counted.
Meanwhile, thousands of demonstrators pressing to install Yuschenko as president are rallying in the capital Kyiv for the third day today.
Yesterday, up to 200,000 opposition supporters gathered in Kyiv for what were peaceful protests.
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