Roman, a worker from Kyiv, agreed with the parliament's decision and said he has no doubt Yushchenko will become the country's next president.
"I think the decision is positive," Roman said. "On the other hand, it doesn't matter if there will be another vote or not, but [Yushchenko] will be the winner without any doubt."
The parliament's nonbinding resolution has no legal force, but it is seen as backing Yushchenko, who claims he was denied victory in the runoff due to electoral fraud.
The parliament also voted no confidence in the Central Election Commission, which has officially declared Yanukovych the winner of the election.
Another supporter of Yushchenko, Jevgenij of Cherkesk, agrees with Parliament's decision. However, he said it is not clear if Yanukovych supporters will peacefully accept the decision, especially if the Supreme Court endorses it.
Vasily Yeriomin from Ivano Frankivsk said the parliament in its majority is loyal to President Leonid Kuchma and Prime Minister Yanukovych. But even the parliamentarians saw the "rising power of the Ukrainian people and had to state that the elections were falsified."
"They accepted the decision under the pressure coming from the people," Yeriomin said. "I don't think they did it under the orders of Kuchma."
There are smaller numbers of Yanukovych supporters in the center of Kyiv. Igor from Kyiv is one of them, but he said parliament made the right decision. He said another vote, if it happens, will yield the same result -- Yanukovych will win.
"I support the decision of the authorities [in parliament]," Igor said. "There should be full democracy, and people who support one or another side took their positions and the election will be fair. It will be done more nicely, more democratically, and there will be no questions and arguments about [who won and who lost]."
Two young men, Sergey and Piotr, bravely walked with two huge Yanukovych flags among a group of Yushchenko supporters. Sergey said parliament's decision is null and void because the body has no right to make declarations on elections.
A painter, Wolodimir Kostin, marching with a small crowd of Yanukovych loyalists, said he supports the parliament's decision. He also agrees that Yanukovych will win if the Supreme Court decides that another vote should be held.
"There is no doubt we will win because the truth is on our side," Kostin said. "The opposition uses [aggressive] slogans. Even the color they use as their symbol -- [orange] -- is a color of aggression, color of war, and color of betrayal. Yanukovych, as you see, uses colors of peace, of truth and hope."
Yanukovych supporters show blue and white.