"To conclude negotiations with the Palestinians during this parliamentary tenure" is the biggest challenge facing Israel, he said.
"Distinguished Arab leaders have told me that a peace accord with the Palestinians would be recognised as a regional peace agreement that includes Israel," he said.
Peres called on Netanyahu to work towards a coalition government composed of parties from across the political spectrum.
"Most of parties voiced a clear preference for a broad national unity government. This is also my request," he said.
Although Likud finished second in the February 10 election, taking one less seat than the centrist Kadima party, Netanyahu has the support of most parliament members.
He already has enough pledges of support from right-wing parties to form a 65-seat majority but he has said that he favours a coalition that includes Kadima, led by Tzipi Livni.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said that Netanyahu has so far had little success in forming a coalition executive, given that Kadima and the left-wing Labour party have played down a partnership with Likud.
"Netanyhau is really desperately trying to get Kadima and Labour on board, to take part in his coalition - particularly Kadima. He does want to get a centrist government, a broad-based government that is stable," she said.
"The problem with having a slender majority ... is that you are really hostage to the whims and particular interests of the small parties that make up that coalition. You only need to alienate one of those parties and they can threaten to pull out."
While Kadima won most support in the election, the Labour party, led by Ehud Barak, suffered its worst performance in a general election in years, finishing fourth in the poll.
Yisrael Beitenu, a far-right party that advocates the construction of illegal settlements in the occupied West Bank, finished third in the poll.
The new parliament is the 18th in Israel's 61-year history, but the fourth to be sworn in over the past decade.
"Israelis are rather used to all this. Under Israeli law there are supposed to be elections every four years but, in practice, they happen a lot more frequently because there are these unstable coalitions," Rowland said.
The rise in support for right-wing parties in Israel comes after the country waged a 22-day war on Gaza.
More than 1,300 Palestinians, at least a third of them women and children, were killed, while 14 Israelis died.