Opposition leader Mr Yanukovych said any new coalition should include his Party of the Regions.
Ms Tymoshenko leads the second largest group in the 450-seat assembly, after Mr Yanukovych's Party of the Regions.
One politician who might be well-placed to ride a wave of social discontent is Viktor Yanukovich, leader of the Party of the Regions, who draws his support mainly from the Russian-speaking south-east.
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Yanukovich's Party of the Regions and its allies are expected to retain a majority in the election, but they are closely trailed, according to some opinion polls, by a bloc that includes Tymoshenko's party.
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By Monday evening, with most of the votes counted, the Party of Regions had about 33 percent of the vote.
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That, and two failed court appeals, has left the ruling party out of the race in Lazio, one of five potential swing regions.
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And Berlusconi, whose center-right party has strong support among the wealthy entrepreneurs of Italy's productive regions, also passed up an opportunity to make a better showing for the center-right.
He wants to put aside intra- and cross-party rivalries in order to secure funding for reconstruction of the tsunami-ravaged regions of north-east Japan.
Berlusconi is using his showman charm to mount a comeback for his People of Freedom party and holds key regions in Veneto and Lombardy that could prove crucial, particularly in the battle for the Senate.
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To rebound, the party is planning a large-scale marketing and outreach campaign over coming months, reaching into neighborhoods and regions of the country where Republicans don't usually fare well, Mr. Priebus will announce, according to his speech.
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