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 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."
Meanwhile, two top EU envoys, Former Polish President Aleksander Kwasniewski and former European Parliament President Pat Cox, headed to Kiev on Tuesday to continue to press for Tymoshenko's release.
The two had previously set Tuesday as a deadline for the bill to be passed, but they have extended their deadlines in the past and the actual start of the summit, Nov. 28, now appears to be the crucial date.
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.
__
Vladimir Isachenkov contributed to this report from Moscow.