Peres, meeting in Jerusalem with British Foreign Secretary William Hague, said there have been some positive developments among Israelis, Palestinians and Arabs in the long and slow peace process, The Jerusalem Post reported.
"This is a critical time for the entire region," Hague said.
Hague said Britain's relationship with Israel had cooperation on many fronts, the Post reported.
But in an interview with British broadcaster Sky News Friday Hague said Israel was losing support in Britain and other European countries because of its settlement activities in the West Bank.
"We strongly disagree with settlements on occupied land," Hague said in the Sky News interview. "Israel is a country we work with in many ways but we do disapprove of settlements."
In advance of another round of meetings with Israeli and Palestinian leaders Friday, Kerry said time is of the essence to revive the stalled Middle East peace process.
"I am convinced, with great humility, that this moment is a critical one for the region and particularly for Israel, for Palestine and for Jordan," Kerry said before meeting with Peres in Jerusalem and then traveling to Ramallah in the West Bank to meet with Palestinian Authority President Mahmoud Abbas and his aides.
The next 18 to 24 months are essential to agreeing on key steps forward in the peace process and the creation of an independent Palestinian state alongside Israel, Kerry said.
Palestinian officials have said they expect Kerry to present a proposal for restarting talks by early June.
Both sides have said they want to talk.
But before Kerry arrived in Ramallah -- his fourth visit to the area in eight weeks -- a Palestinian official told The New York Times he saw no indication Israel would consider meeting Palestinian requirements to resume the long-stalled talks.
A key requirement is that Israel's continued settlement construction in the West Bank be halted.
"The next days and weeks are critical, and it's important everyone stays focused," she said after meeting with Kerry.
Livni acknowledged differences within Prime Minister Binyamin Netanyahu's 2-month-old coalition government, pointing out the right-wing Jewish Home Party member rejects the idea of a Palestinian state.
But she said Netanyahu was fully aligned with Kerry's effort.
Netanyahu said before meeting with Kerry resuming peace talks was "something I want. It's something you want. It's something I hope the Palestinians want as well."
The official Palestinian news agency WAFA said after Kerry and Abbas met the Palestinian leader again raised "key issues" including Israel's settlement construction, "Israeli attacks" in East Jerusalem, settler violence and Israel's detention of Palestinian prisoners.