A total of 203 MPs voted for the motion, with 226 required for it to pass.
The pro-Russian 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 parliament.
Tymoshenko on Thursday addressed parliament with a report on the government's work to overcome the economic crisis.
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.
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.