EU Parliament President Martin Schulz said the Cox-Kwasniewski mission would be extended right up to the Nov. 28-29 Eastern Partnership summit in Vilnius, Lithuania.
The two envoys said next Tuesday's parliamentary session in Kiev will be crucial. "It can be decisive in yielding a settlement but risks also to result in stalemate and a non-productive blame game," they said.
Opposition leaders accused Yanukovych and his allies in parliament of purposely sabotaging the long-awaited EU deal.
Russia staunchly opposes the signing of the EU agreement and has used threats, sanctions and offers of price discounts in an attempt to lure Kiev away from the EU and into a Moscow-led customs union instead.
After the session was closed, parliament erupted with angry chants of "Shame! Shame!" from opposition lawmakers, some dressed in white sweaters that read "Freedom to Ukraine" and others wearing red sweaters reading "Ukraine is Europe."
"You are ready only for political persecution, blackmail, pressure and to hold on to your power," opposition leader and top Tymoshenko ally Arseniy Yatsenyuk said, referring to Yanukovych. "We, however, want the power to belong to the people of Ukraine."
Cox and Kwasniewski also noted "a chronic lack of mutual trust and confidence between the parties of government and opposition." EU Commission spokesman Peter Stano urged Ukraine to show "determined action and tangible results" for the agreement to be signed.
Meanwhile, in another sign that Kiev might be tilting toward Moscow, Prime Minister Mykola Azarov told his Cabinet on Wednesday that normalization of ties with Russia is Ukraine's top priority.
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Raf Casert contributed to this report from Brussels.