Thousands of protesters have staged fresh demonstrations in Ukraine over the political crisis which is dividing the country.
Members of Ukraine's Communist Party marched for Mr Yanukovych
PM Viktor Yanukovych has told the cabinet not to prepare for a snap election called by the president until a ruling by the constitutional court.
Mr Yanukovych's supporters held protests in the capital Kiev and in his eastern power base of Donetsk.
President Viktor Yushchenko's office says poll preparations are going ahead.
Opponents of the president are continuing to come out onto the streets, says the BBC's Helen Fawkes, in Kiev.
Supporters of the prime minister were joined by the Communist and Socialist parties for a large rally in Kiev's main Independence Square, our correspondent says.
Some marched to the president's office and surrounded the building.
Supporters of Mr Yushchenko, numbering a few hundred, had also gathered at the scene but there have been no signs of violence.
Parliament, where the prime minister has a majority, continued to sit in defiance of Mr Yushchenko's decree on Monday to dissolve the assembly.
The prime minister's supporters have urged the constitutional court to rule on whether or not the president had the right to dissolve parliament.
The pro-Western Mr Yushchenko accuses his pro-Russia rival of trying to usurp power by increasing his parliamentary majority in an unconstitutional manner.
The pair met on Tuesday in Mr Yanukovych's office, but Mr Yushchenko failed to gain his agreement to implement the decree, which orders an early poll on 27 May.
The political stand-off has echoes of the 2004 Orange Revolution which swept Mr Yushchenko to power, although so far fewer protesters have taken to the streets.
On Tuesday, Mr Yanukovych told supporters massed outside parliament that he would try to force a presidential election if Mr Yushchenko persisted with plans for a snap parliamentary poll.
"He should understand that the only way out is looking for a compromise at the negotiating table," he said.
Mr Yushchenko accuses Mr Yanukovych of trying to usurp his power by illegally luring pro-Western lawmakers over to his coalition to increase his parliamentary majority.
Under the constitution, only factions - not individuals - can change sides. But last month 11 lawmakers allied with Mr Yushchenko switched sides.
If Mr Yanukovych gains 300 deputies in the 450-seat house, he will have the power to overturn presidential vetoes and oversee new constitutional change.
Mr Yushchenko became president in January 2005, following the pro-democracy Orange Revolution which overturned a rigged victory for Mr Yanukovych.
But Mr Yushchenko was forced to accept his rival as prime minister after his allies failed to win a majority in the March 2006 parliamentary election, and the two men have repeatedly clashed.