With the ruling party and opposition in the Verkhovna Rada struggling to find a compromise on the bill, Russian Foreign Minister Sergei Lavrov accused the EU of exerting "brazen" pressure on Ukraine to choose between Moscow and the West.
In a session personally attended by EU Enlargement Commissioner Stefan Fuele, the Verkhovna Rada failed to even debate the bill that would allow Tymoshenko to seek medical treatment in Germany.
Freeing Tymoshenko in some form is a crucial condition set by EU leaders for Ukraine to sign an Association Agreement -- a first step to membership -- at a summit in Vilnius on November 28-29.
Signing the Association Agreement would mark a historic break by Ukraine from Russia, its master both in the Tsarist and Soviet eras, which has been infuriated by the prospect of Kiev's close integration with the EU.
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"Get over your fear and on Thursday vote for these bills," he said, adding that the opposition was ready to vote for a text that suited the Regions Party.
But Regions Party faction chief Olexander Efremov said there was still no agreement on a single text that could be voted on by the Rada.
Tymoshenko, the fiery opposition leader who rose to fame during the 2004 Orange Revolution and is an arch-rival of Yanukovych, was sentenced in 2011 to seven years in prison on abuse of power charges, prompting international criticism of the case as politically motivated.