Opposition supporters led by former Prime Minister Yuliya Tymoshenko are expected to hold a rally in Kyiv's central Independence Square to support Yushchenko's call for early elections.
Supporters of Prime Minister Viktor Yanukovych's ruling coalition are also expected to demonstrate in the same place. They argue that new elections would not be necessary.
The rival protests are likely to go ahead despite a ruling by a Kyiv court banning all demonstrations. The March 30 ruling upheld a decision by city authorities to ban all the demonstrations in the square.
The court said it made the decision to "avoid any possible clashes." Opposition leaders vowed to appeal the ruling and to go on with their plans.
Yushchenko issued his threat on March 29, accusing Yanukovych's ruling coalition of violating the constitution after parliamentarians once allied with the president switched sides to Yanukovych's coalition.
Opposition supporters preparing for today's demonstration on Independence Square (RFE/RL)
He accused the pro-Russian coalition of trying to "usurp power" by persuading pro-Western lawmakers to switch sides.
Yushchenko today reiterated his stance during a conference of his party's delegates.
Opposition leader Yuliya Tymoshenko met with Yushchenko on March 30. After the meeting, Tymoshenko spoke in support of Yushchenko's call for early elections.
"We stated [to President Yushchenko] all the legal grounds and political reasons for dissolving [parliament] and we appealed to the president: either we dissolve this parliament immediately, or, unfortunately, what such unity rallies [held by the ruling parliamentary coalition] are going to offer to the people is national unity with the mafia," Tymoshenko said.
Pro-Western Yushchenko and Moscow-backed Yanukovych have been at loggerheads since the prime minister emerged as the winner of parliamentary elections in March 2006.
The Blue Camp
Thousands of Yanukovych supporters rallied yesterday in Kyiv and other cities. Police estimated that as many as 15,000 people took part in the rally.
Yanukovych supporters rallying in Kyiv on March 30 (epa)
Yanukovych, addressing demonstrators in Kyiv, accused the opposition of seeking to bring about early parliamentary elections "at any price."
"A small group of those disgruntled by the fact that they were not supported by the people and who found themselves outside the bodies of power have been trying -- almost since the early days following the [parliamentary] elections -- to bring closer the date of parliamentary elections at any price, in violation of the laws and the constitution of the country," Yanukovych said.
Yushchenko became president when he defeated Yanukovych after mass protests known as the Orange Revolution forced a repeat of the country's flawed 2004 presidential election. Yanukovych had been declared the winner of the first vote, in November 2004.
Yushchenko favors Ukrainian integration with the West, including NATO.
Yanukovych, backed by Russian speakers from the east and south of the country, is opposed to NATO membership and favors closer links to Moscow.
(RFE/RL's Ukrainian Service contributed to this report)