Yanukovych has rejected the order and urged the legislature to continue working while it waits for the Constitutional Court to rule on its legality. (A gallery of images from Kyiv on April 6 and April 7.)
The pro-Western Yushchenko ordered the dissolution of parliament accusing the pro-Russian supporters of Yanukovych of violating the constitution and seeking to usurp power.
Serhiy, a Yanukovych supporter, said demonstrators would remain on the streets until the president backed down.
"We will stay here until [Yushchenko] cancels his decree," Serhiy said. "Let him cancel the decree, which is illegal. We consider that the parliament [is in power]."
Talks between Yushchenko and Yanukovych this week failed to yield a compromise.
The Kremlin said Russian President Vladimir Putin telephoned Yushchenko on April 6 to express his concern over the potential economic effects of the crisis and urge a constitutional solution.
(with material from agency reports)