The most probable date for a national election is February 17, 2009.
Earlier on Sunday evening, Livni's last-minute decision to postpone the meeting with Peres until 5:30 p.m., set off speculation that coalition negotiations were still in the works.
According to reports, Knesset speaker Dalia Itzik had requested the delay in a last-ditch effort to salvage talks to form a new government.
Earlier, Livni had said that she decided to end her bid to form a coalition because she felt she had to "draw the line" in the concessions she was willing to other parties.
"After the primaries I said that I believed in stability and was committed to seeing through the process of forming a government. Recent days have seen coalition demands become impossible, and there was a need to draw the line. To say 'no more,'" Livni said during the weekly cabinet meeting.
"I was prepared to pass budgets I believe in for needy families and social [causes]. But when it became clear that every person and every party was taking advantage of the situation to make illegitimate demands - both economic and diplomatic - I decided to put a stop to it and go to elections.
"That is the essence of Kadima. On this basis we formed Kadima and on this basis we will continue to act in unison and win. A united Kadima that proves that it acts according to what's right will win the next elections," Livni said.
Livni was originally scheduled to meet Peres at 5:00 p.m., but the meeting was moved up to 2:00 p.m. However, as reporters waited at the entrance to the President's residence in Jerusalem, an announcement was made that the meeting had been postponed to 5:30 p.m.
Sources in Kadima said Livni made the decision at a meeting held late Saturday night with her advisers, among them Transportation Minister Shaul Mofaz.
The move came after Shas and Degel Hatorah, which constitutes half of the United Torah Judaism faction in the Knesset, announced over the weekend that they would not join a Livni-led government.
"I'm sick of this extortion," Livni was quoted as telling her advisers. "We'll see all these heroes in 90 days."
Shas announced on Friday that it had rejected Livni's offer to join her coalition, because its Council of Torah Sages advised against it.
"The Council of Torah Sages decided this morning, after a telephone survey and in accordance with the directives of Rabbi Ovadia Yosef, that Shas will not join the government," Shas chairman Eli Yishai told reporters outside his Jerusalem home. "The decision is final."
Prior to the press conference, Shas had released a statement in which it said: "Throughout the negotiations, Shas hasn't asked for political upgrades or fancy titles. It has asked for only two things: a profound assistance to the weak socioeconomic classes living in Israel and the protection of Jerusalem," the statement read.
"Our negotiators proposed solutions for these two issues, but their opinion was not accepted," the statement continued.
Palestinians expressed concern Sunday that Livni's decision could put already fragile peace talks in limbo for months until the elections are held. The balloting could also clear the way for opposition leader Binyamin Netanyahu, who rejects sweeping territorial concessions to the Palestinians, to reclaim the premiership.
An aide to Palestinian Authority President Mahmoud Abbas warned that the Israeli political turmoil could threaten peacemaking.
"Time is precious. The next few months will be wasted because of [Israeli] elections and the US elections," Nabil Abu Rdeneh said.
A meeting between Prime Minister Ehud Olmert and Abbas, which had been scheduled for Monday, was postponed until further notice because of the Israeli political upheaval, Abu Rdeneh said.