But Yanukovich, back in power after being defeated by the president after pro-Western "Orange Revolution" protests, said the president had no grounds to dissolve the assembly in order to hold a new parliamentary poll.
Politics in Ukraine, in a stalemate since the president reluctantly appointed Yanukovich prime minister last August, has suddenly become highly charged by the defection to cabinet ranks last week of one his most prominent "orange" supporters.
The president said parliament had "usurped power and betrayed the constitutional order". He singled out the prime minister's suggestion that his coalition could soon marshal 300 of 450 votes in parliament, enough for further constitutional change.
"If some political forces say out loud that they can get 300 votes in a parliamentary coalition, let us then make a political decision, please," he told a news conference in eastern Ukraine.
"Let's hold a parliamentary election so you can appeal to the country. If they indeed love and trust you and give you those 300 votes, then you can speak about such a majority in Ukraine's parliament."
In a statement issued earlier in the day, the president said parliament in the past year had done nothing in the interest of Ukrainians and "again produced empty promises and declarations".
Yushchenko was making his second attack in two days on institutions underpinning the prime minister. On Wednesday, he described the government as illegitimate.
Yanukovich, friendlier to Moscow than the president, ruled out any dissolution of parliament.
"First of all, I don't believe the president will do this," he told reporters. "Secondly, I believe he cannot do so as the constitutional court will never agree this is within the framework of the constitution."
The prime minister's backers are to rally in Kiev on Friday.
The opposition, led by former prime minister Yulia Tymoshenko, the president's revolution-era ally sacked after eight months in office, have long called for a new election. Its supporters are to hold a demonstration of their own on Saturday.
The president appointed Yanukovich prime minister last year after his own allies scored badly in a parliamentary election and were unable to form a government.
Yanukovich initially promised to leave the president's policies intact, including long-term membership of Nato and the European Union, but the two have sniped endlessly over powers.
The president's powers, reduced by constitutional change approved at the height of the 2004 mass protests, were further curbed by legislation approved by parliament late last year. The prime minister can now count on about 250 seats in parliament.
Source: Independent Online