Ukraine's President Viktor Yushchenko is willing to suspend his decree dissolving parliament and ordering an early 27 May election, an aide says.
A political agreement between the two Viktors might be possible
Security adviser Vitaly Hayduk said Mr Yushchenko was prepared to let the rival members of parliament negotiate a new date for elections.
Mr Yushchenko has been locked in a long-running power struggle with Prime Minister Viktor Yanukovych.
Thousands of the two rivals' supporters are demonstrating in the capital Kiev.
"The president does not rule out that the presidential decree can be suspended, not repealed but suspended, thus giving a chance to come up with a timetable which would give political forces a chance to get ready for the election process," Mr Hayduk said at a press conference on Wednesday.
Communists have been rallying for Viktor Yanukovych in Kiev
Mr Yushchenko dissolved parliament on 2 April, accusing Mr Yanukovych of usurping power by luring deputies into his bloc in parliament. Mr Yanukovych's bloc favours closer ties with Russia.
Mr Yanukovych, supported by a majority in parliament, opposed the president's move and took the matter to the constitutional court.
On Tuesday, judges from the court said they were unable to reach a decision because of political pressure and asked for police protection.
The rivalry between Mr Yushchenko and Mr Yanukovych dates back to the 2004 liberal Orange Revolution which swept Mr Yushchenko to power, overturning a Yanukovych election victory which was widely condemned as fraudulent.
Constitutional reforms carried out as a result of the Orange Revolution weakened the president and strengthened parliament - but Mr Yushchenko and Mr Yanukovych have clashed over the details.