However, Kuchma continues to insist that the opposition agree to his demands concerning constitutional amendments, putting any deal in doubt.
Kuchma announced after the talks that he is prepared to disband the Central Election Commission that was responsible for overseeing last month's fraudulent elections.
Kuchma, speaking to reporters, said also that he is ready to support changes to the election law in advance of a repeat of the poll, due on 26 December.
"[We] agreed on the need to introduce amendments to the law on electing Ukraine's president that would envisage introducing a mechanism for conducting transparent and fair elections, making abuse and fraud impossible," Kuchma said.
The changes would include eliminating the use of absentee ballots and voting from home -- two measures that the opposition says were widely used to falsify the second round of voting on 21 November.
But Kuchma indicated that the opposition continues to refuse his proposal to amend the constitution to reduce the powers of the president and transfer most authority to the parliament. Kuchma said that as a result of this deadlock, no deal was reached on the opposition's third demand -- the resignation of the current government, headed by Prime Minister Viktor Yanukovych.
The opposition says that Yanukovych's departure is especially important, as it would deprive the prime minister of what are called "administrative resources" to unfairly influence the campaign in the three weeks leading up to the election.
"The differences mainly concern a package voting [in the Ukrainian parliament] on political reform on the one hand and government resignation on the other hand," Kuchma said.
The opposition said that any amendment to the constitution should be carefully considered and not rushed through three weeks before the election. Yushchenko and his backers accuse Kuchma of seeking the constitutional changes to deprive Yushchenko of power, should he emerge as the winner of the poll.
Parliament was due to reconvene today but it remains unclear if legislators will be able to accomplish much, as long as Kuchma and the opposition fail to reach a comprehensive agreement. It is up to Kuchma, for instance, to nominate new members to the Central Election Commission for parliamentary approval.
In another development, Yanukovych reemerged in public at a rally in Kyiv yesterday after days out of the limelight. Yanukovych told his supporters that -- far from representing change -- his rival Yushchenko, who once served as the country's central banker and prime minister, is a man of the past.
"Today, I can say openly that two types of state power have existed in our country for the last two years -- old power and new power," Yanukovych said. "So our citizens should make their own conclusions whether Yanukovych is a candidate of the new power or the old power. I am sure that Yushchenko represents an attempt by the old power to seek revenge."
U.S. Secretary of State Colin Powell, speaking today in the Bulgarian capital Sofia, before a meeting of the Organization for Security and Cooperation in Europe, said the United States is not interested in carving out a sphere of influence in Ukraine.
Responding to comments made by Russian President Vladimir Putin yesterday, Powell said that the United States wants an outcome in Ukraine that reflects the genuine will of its people.
(news agencies)[To see an archive of RFE/RL's full coverage and analysis since the Ukrainian crisis began, click here.]