A total of 203 MPs voted for the resolution, with 226 required for it to pass.
The Party of Regions demanded on Thursday early parliamentary and presidential elections.
"There is only one way out of this political crisis. We need to change the president, the government and the parliament," party leader Viktor Yanukovych said in the parliament.
A public opinion poll conducted by Ukraine's influential Strategic Studies Institute on January 28 - February 3 showed that Yanukovych would gain the most votes if presidential elections were next Sunday, RIA Novosti reproted.
A total of 23.2% of respondents would vote for Yanukovych, 12.9% for current premier Tymoshenko, 9.9% for ex Supreme Rada Speaker Arseniy Yatsenyuk and 8.7% for incumbent President Viktor Yushchenko.
A total of 2,012 people were polled in all Ukrainian regions. Statistical margin of error was 2.3%.
The next presidential elections are due to be held in late 2009 or early 2010, with the exact date to be set by parliament.
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