The two rallies were held 300 meters from one another, separated by metal fences and riot police in protective gear.
The rival protests went ahead despite a ruling by a Kyiv court banning all demonstrations to "avoid any possible clashes."
Shows Of Strength
The rallies were planned as a result of President Yushchenko's threat on March 29 to dissolve parliament and call for early elections.
Several thousand pro-Yushchenko demonstrators filled Independence Square in downtown Kyiv.
"I support people who say there's a need to dissolve the parliament because the so-called coalition doesn't keep its promises and just does nothing," one demonstrator said. "I support opposition parties, such as the Yuliya Tymoshenko Bloc or Our Ukraine. I think [the dissolution of parliament] will change something."
On nearby European Square, thousands of Yanukovych supporters demonstrated against early elections and the dissolution of parliament.
Many of them had traveled to Kyiv from Ukraine's eastern regions, where Yanukovych has his power base.
"Why did we come? Just to support the government we have now. That's why we came," one participant said. "And nobody paid us for that -- it's not true they've 'bought' us. Look, I even took my own snacks with me, I can show you, from where I live in Dniprodzerzhynsk (an industrial city in Central Eastern Ukraine). And don't mention I'm 67 years old, I'm satisfied with Yanukovych and his government, and all of our Ukrainian people, everybody, is for him!"
Speaking today at a conference of the pro-presidential Our Ukraine party, Yushchenko reiterated his readiness to dissolve parliament and call new elections.
"If the actions of the majority in parliament do not return to a constitutional basis, I will sign a decree dissolving parliament."
Yushchenko first issued his threat on March 29, after parliamentarians once allied with him switched sides to Yanukovych's coalition.
He also accused the pro-Russian coalition of trying to "usurp power" by persuading pro-Western lawmakers to switch sides.
Under the constitution, the coalition can only be formed on the basis of factions -- not individual deputies or small groups of lawmakers.
Today's rallies came after thousands of Yanukovych supporters demonstrated March 30 in Kyiv and other cities.
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. His opponent, Yanukovych, had been declared the winner of the initial vote.
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 Belarus, Ukraine, And Moldova Report
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