Parliament speaker Volodymyr Rybak told legislators that a vote on the bill would be put off until Thursday, a sign that President Viktor Yanukovych is continuing to maneuver between the EU and Russia, which has strongly opposed the EU-Ukraine deal and appears to be working both openly and behind the scenes to derail it.
Yanukovych has resisted strong Western pressure to pardon Tymoshenko, and as a compromise solution the EU has asked the Ukrainian parliament, dominated by pro-presidential lawmakers, to adopt a law allowing Tymoshenko to fly to Germany for treatment of a back problem.
Tymoshenko's top ally, opposition leader Arseniy Yatsenyuk, called on the pro-Yanukovych party in parliament to adopt the bill on Thursday and for Yanukovych to immediately sign it into law right in the parliament hall.
"This is the will of the Ukrainian people who want Ukraine to become a European country," Yatsenyuk told Parliament.
Tymoshenko, the charismatic heroine of the 2004 Orange Revolution and a top rival of Yanukovych, is serving a seven-year prison sentence on charges the West calls political.
The EU has indicated it does not want to sign a free trade and a political association agreement with Ukraine at a summit in Vilnius, Lithuania, next week, if Tymoshenko remains in jail.
On Monday German Chancellor Angela Merkel again urged Ukraine to take "credible steps" ahead of the summit and warned that the EU will not be content with "lip service."
Russia has seen the proposed EU deal with Ukraine as an encroachment on its home turf and responded with a mixture of promises and threats.
It has offered Ukraine cheaper prices for natural gas, which has become a source of fierce arguments and led to shutdowns of Russian gas exports to the EU via Ukraine in the past.
At the same time, Russia has warned that it would protect its market with higher tariffs on Ukraine's imports if it signs the free trade deal with the EU.
The EU has warned Russia against applying pressure on Ukraine.
On Tuesday, Russia's Foreign Minister Sergey Lavrov rejected the EU criticism as "unclean," arguing that Russia fully respects the sovereignty of its neighbors and accusing EU officials of exerting "shameless pressure" on the ex-Soviet nations.
Lavrov said that the EU rhetoric boils down to offering ex-Soviet nations a choice between a "dark past" with Russia or a "bright future" in association with the EU.
"They say: you need to make a choice, and you must choose the EU, or else you will get lost," he said.