Yushchenko said in a live national broadcast on Wednesday that the move a day earlier amounted to "a political and constitutional coup".
He said a new governing coalition should be formed.
Tymoshenko said: "The president and his office has used every means to ruin the coalition."
"It is a pity that the president behaves with no responsibility. The coalition split yesterday, by his own decision," she told a cabinet meeting.
Divide over Russia
In a parliament session on Tuesday, the ruling coalition also failed to agree on a joint declaration about the war between Russia and Georgia, which like Ukraine, is bidding to join Nato and the European Union.
Yushchenko has accused Tymoshenko of "high treason and political corruption" for allegedly siding with Moscow over the conflict in Georgia last month, a charge she has denied.
If the pro-Western allies Our Ukraine and Tymoshenko Bloc do not re-unite and the decision to split comes into effect, members of parliament would have a further 30 days to form another coalition government.
|Deputies of 'Our Ukraine' party hold a Georgian flag in parliament [AFP]
The president would have the right to dissolve parliament if talks failed.
Tymoshenko has long had shaky relations with Yushchenko despite their alliance in the peaceful protests known as the Orange Revolution of 2004.
She is believed to be planning to run against Yushchenko for president in elections due in 2009 or 2010.
Tymoshenko abstained from a vote in Ukraine's security council last month imposing restrictions on the movements of Russia's Black Sea fleet, which is based in southern Ukraine and was involved in military action against Georgia.
European officials including Bernard Kouchner, the French foreign minister, and Olli Rehn, the EU enlargement commissioner have warned Ukraine could be the next target of political pressure from Russia in its mounting stand-off with the West.
Dick Cheney, the US vice president, was due to visit the capital Kiev this week as part of a four-nation tour to support US allies Georgia and Ukraine.
Cheney arrived in oil-rich Azerbaijan on Wednesday at the start of his tour.