Pro-Russian Yanukovych has defied the order and hundreds of his supporters have camped outside the parliament for more than a week.
The two men have feuded since 2004, when the mass protests of the Orange Revolution brought Yushchenko to power after a presidential election win in Yanukovych's favour was declared fraudulent.
"The presidential decree is unconstitutional. That's not my president and his party is against the people," Georgy Yershov, a 70-year-old man from Dnipropetrovsk in eastern Ukraine, said at the protest.
Yanukovych has called on the 18-judge constitutional court to rule on the legality of the presidential decree.
On Tuesday, the court announced that it would not start examining the case until April 17 and five judges from the court, three of them Yushchenko appointees, said they were being put under undue political pressure.
Yushchenko has decreed early elections for May 27. The president has said he will not rescind his order, though he has admitted the date for the elections could change.
"The date is one of those issues that can be resolved during political negotiations," Yushchenko said on Tuesday.
"The main thing for us is to find a constitutional answer regarding the date so that [the elections] cannot be revised later."
"Honest Court, Honest Elections," "East and West Together," "No to the Criminals in Power!" read the placards held by the pro-Yushchenko activists at Wednesday’s rally.
"We're here to support the president and his decision... There is a lot of pressure against the judges," said Nadya Kryvonos, a local deputy from Kremenchug in central Ukraine.
"We want to say: do not be afraid, we are with you."