The move launches what is expected to be a tough race between Livni, seen as a moderate, and Benjamin Netanyahu, an opposition leader viewed as a hardliner.
"The confidence we have in the government has been weakened," Peres told parliament, in an apparent reference to Ehud Olmert, the prime minister, who is stepping down amid corruption allegations.
Olmert will remain interim prime minister until a new government is in place.
"International developments present complex challenges for Israel... It is in your power to turn this election to good use," he added.
Jacky Rowland, reporting for Al Jazeera from Jerusalem, said: "So far good news for Livni. For the first time, Kadima is ahead in the opinion polls. But this is a narrow lead and polls like this are not scientific."
Kadima, the left-of-centre Labour and the right-wing Likud were already mapping out the outlines of their political agendas for a campaign that is likely to focus on the future of the Middle East peace process.
"We have been in a period of uncertainty for several months and, therefore, the elections should take place as soon as possible," Livni told parliament ahead of Peres' announcement.
Livni said she instructed her party to discuss a date for the vote with other factions after abandoning efforts to form a coalition because she would not entertain the religious Shas party's conditions.
"I was ready to pay a certain price ... but I wasn't ready to mortgage the future of Israel," Livni said after Shas set budgetary conditions and insisted the fate of Jerusalem could not be included in peace talks.
Livni said she would maintain Olmert's policies favouring the creation of a Palestinian state alongside Israel, but with the Israel retaining its major settlements in the West Bank, which are illegal under international law.
Both Israel and the Palestinian had pledged to try to reach a deal before George Bush, the US president, leaves office in January, but the talks have made little visible progress.
Salam Fayyad, the Palestinian prime minister, said that peacemaking was "teetering" because of continued settlement construction and the construction of Israel's controversial separation barrier.