The deadlock exposed the fragile nature of a 227-member coalition of two parties to emerge from a September election - Tymoshenko's bloc and Yushchenko's Our Ukraine party.
On Tuesday, the Rada narrowly rejected Tymoshenko amid accusations of vote tampering.
Viktor Yanukovich, the outgoing prime minister and 2004 presidential rival, said Tuesday's vote showed an "orange" coalition had no future.
He repeated his call for a "broad coalition" of his Regions Party and some of Yushchenko's supporters.
"Voters must at last get an answer on whether the coalition of 227 can take responsibility for the country. Let's make it clear, yes or no," he said in a statement on his website.
"I hear talk in the corridors that Tymoshenko doesn't have support and time is not on Yulia Tymoshenko's side"
Anna Herman, senior member of the Regions Party
However, Anna Herman, an ally of Yanukovich in the Regions Party, suggested the party might agree to an "orange" candidate other than Tymoshenko.
"We must find ways to resolve this problem. Nominating another candidate for prime minister could be a way out," she told reporters outside the chamber.
"I hear talk in the corridors that Tymoshenko doesn't have support. And time is not on Yulia Tymoshenko's side."
But Tymoshenko's allies ruled out any such deal.
"There are no grounds to change this candidature," said Ruslan Knyazevych of Our Ukraine. "That would mean altering the agreement on forming our democratic coalition. And it would seem to me that's impossible."
Tymoshenko said all 227 coalition members had backed her on Tuesday, but tampering prevented two from registering their votes.
The SBU security service, summoned to investigate, said checks revealed no interference in the system.
Oleksander Turchinov, one of Tymoshenko's lieutenants, told reporters any new vote should be taken by a show of hands.
"The speaker would call on each member to raise his hand and say publicly whether he is for or against," Turchinov said.
Named prime minister days after Yushchenko's inauguration, she fell out with the president and was sacked seven months later.
She spooked investors in office by calling for a major review of privatisations and by trying to influence markets.
The two reconciled for the September election that had been intended to end three years of political turmoil.