A senior aide to Ukrainian President Viktor Yushchenko says the president is willing to freeze his order to dissolve parliament and hold early elections.
Security council secretary Vitaly Hayduk said Wednesday suspending the order would give parities more time to prepare for a new vote.
But Mr. Yushchenko's chief political rival, Prime Minister Viktor Yanukovych, told thousands of supporters in Kyiv that if there are early parliamentary elections, there must also be an early presidential vote.
President Yushchenko ordered parliament to dissolve last week after accusing Mr. Yanukovych of illegally persuading lawmakers to join his coalition, reducing Mr. Yushchenko's parliamentary support.
The president accuses Mr. Yanukovych of violating the constitution.
Parliament has so far refused to dissolve or authorize funds for a new election.
Ukraine's Constitutional Court holds hearings next week on the legality of President Yushchenko's order.
Tension between the president and prime minister has been simmering since 2004, when the two men were rivals in a controversial presidential election. Mr. Yanukovych won the election, sparking huge street protests by Yushchenko supporters, who called the vote fraudulent. A court ordered a new election, which Mr. Yushchenko won.
Some information for this report was provided by AFP and AP.