"For the sake of a unity government, I'm forgoing the rotation agreement," Lapid announced during a faction meeting in Jerusalem, shortly before the new Knesset was sworn in.
"There won't be a rotation deal with three people," Lapid said. "That's not serious. Running a country is a serious matter... there won't be another election."
Lapid also called on Prime Minister Benjamin Netanyahu to step aside due to his criminal investigations and allow a new leader to emerge for Likud. Ntenayhau's perceived greatest rival in the party, Gideon Sa'ar, said Thursday that he would be willing to run a party leadership primary.
Lapid called the prime minister the biggest obstacle to forming a unity government between Blue and White and Likud - the two largest parties after the September 17 elections.
Yisrael Beytenu leader Avigdor Liberman, who along with President Reuven Rivlin has been calling for a unity government since the deadlocked elections, called Lapid's decision a "smart and noble" move that was in the best interests of the country.
Lapid and Gantz agreed earlier this year to rotate the premiership if their political alliance succeeded in heading the next government.
According to the deal, the first two years would have gone to Gantz while Lapid was to take over halfway and finish out the mandated four-year term.
Gantz, who took the stage before Lapid at the party faction meeting, told reporters that the country has "been busy for too long with division," and urged an immediate formation of a government under his leadership.
Neither Netanyahu's right-wing bloc nor Gantz's center-left alliance has enough Knesset members to form a majority coalition.
The Likud has repeatedly accused Lapid of trying to scupper its unity government talks with Blue and White, accusing him of allowing his determination to become prime minister drag the country into an unpredecented third round of elections within a 12-month period.
Liberman said Wednesday that if there were no progress on unity talks between Likud and Blue and White before Yom Kippur next week,
"Even if new elections are held, the political map will not change significantly, and therefore an informed solution must be reached, leaving all personal and ego considerations aside," he said.
Netanyahu, who was last week given 28 days by Rivlin to form a government, met Thursday morning with Liberman, although Likud said the talks failed to lead to a breakthrough.
Moran Azulay and Kobi Nachshon also contributed to this report