"Today we are two different teams," said Tymoshenko, who Yushchenko dismissed from her post on Thursday, just six months before Ukrainians vote in a new parliament in March. "I think these two teams will go their own way."
But she said "it does not mean it will be a war, Viktor Yushchenko and I will go to the elections on parallel paths", adding however that "I won't go into an election with people who have so discredited Ukraine".
Tymoshenko's move deals a huge setback to Yushchenko. Her popularity rivals his, and for many Ukrainians it is Tymoshenko - with her fiery speeches and chic style - who came to symbolise the ideals of last year's so-called Orange Revolution.
She controls a 41-person bloc in parliament - smaller than Yushchenko's combined forces of 96, but still a major force - and is likely to trigger at least a few high-profile defections to her side.
Tymoshenko blamed the circle around Yushchenko for her government's dismissal, and the breakup of their union.
"I am sure it is not the president, it is his team," Tymoshenko said, but she also had harsh words for Yushchenko, accusing him of turning against her in favour of allies that she called corrupt.
"I won't go into an election with people who have so discredited Ukraine"
Former Prime Minister
Yushchenko said on Thursday that he had dismissed Tymoshenko's seven-month old government because it was too embroiled in internal bickering and losing sight of their Orange Revolution promises.
He also accepted the resignation of his close ally, chief of the Security and Defence Council Petro Poroshenko.
Yushchenko on Friday appealed to the leaders of all parliamentary parties to support his acting prime minister, Yuri Yekhanurov. He promised regional leaders that Yekhanurov would continue pursuing the Orange Revolution's goals.
Lawmakers were expected to vote on Yekhanurov's nomination in the next two weeks.
Yekhanurov pledged to continue the reforms begun by his predecessor, but said he would refrain from the heavy state intervention Tymoshenko was criticised for.
"There will be no hand-steering of the economy," he said.
The Russia-born Yekhanurov also pledged he would improve relations with neighbouring Russia, which have been strained since the tumultuous presidential election.