Bold choices are needed to coax the Middle East peace process back to life, including bringing Hamas off the sidelines, which may risk tearing the new Israeli cabinet apart, experts say.

Much will also depend on what legacy Israeli Prime Minister Benjamin Netanyahu, newly-elected for a third term, decides he wants to leave for the history books.

With a renewed focus on the Middle East following US President Barack Obama visit to Israel last week backed by shuttle diplomacy by new Secretary of State John Kerry, there is hope of reinvigorated efforts to reach a peace deal.

But the challenges are huge, and experts at a Brookings Institution debate Thursday warned that new realities on the ground particularly in the wake of the Arab Spring demanded fresh, creative thinking.

"If we're going to have a final status agreement, it will take a leadership act of the highest order by Netanyahu," said Itamar Rabinovich, a former Israeli ambassador to the US and a professor at Tel Aviv University.

"For this he will have to break his coalition," he said, arguing that Netanyahu had been lumped with a cabinet he didn't want and might welcome the chance, under outside pressure, to dump it.

After six weeks of negotiations, Netanyahu unveiled in mid-March a coalition dominated by the hawkish Likud-Beitenu and its new national-religious ally Jewish Home, a far-right faction that is the party of choice for settlers.

Jewish Home leader Naftali Bennett has openly opposed a Palestinian state -- which will put intense pressure on any moves by Netanyahu to resume the negotiations under US stewardship.

The burgeoning settlements have been a major obstacle to bringing the Palestinians back to the table, with Palestinian president Mahmud Abbas demanding a freeze on all new settlement construction.

But Natan Sachs, a fellow at the Saban Center for Middle East Policy at Brookings, pointed to "voices out of the prime minister's office... that Israel might be going towards what it considers to be a quiet freeze" to avoid further global outcry.

Politically, the Palestinians are just as divided as the Israelis, torn between Abbas's Fatah leadership which controls the West Bank and the militant Hamas which rules the Gaza Strip.

Any moves to resume the peace talks will by necessity have to involve some kind of reconciliation with Hamas, both with the Palestinians and with the international community, argued Khaled Elgindy, a former adviser to the Palestinian leadership on the negotiations with Israel.

"Islamists matter, whether they are in the opposition to the government, or whether they're the ruling party. You have to take them into account, and that is especially true in the Palestinian case," said Elgindy, also a fellow at Brookings.

If Kerry decides to go full tilt for a peace deal, he will have to recognize "that the popular will is relevant, and is an actor at the table."

Even if Hamas did not want to sit down and negotiate directly, "they can't be ignored, or wished out of existence," Elgindy said.

"They're there, and if they're not in the process in some broad sense... then they become part of the problem."

He argued there was even broader support for a two-state solution in the Gaza Strip than there was in the West Bank, where the majority believe it is no longer viable.

But Washington is firmly opposed to direct engagement with Hamas, which has been on a US blacklist as a foreign terrorist organization since 1997.

Third-party countries which have some liaison with Hamas and which are US allies could be tapped to help sound out Hamas's true intentions, suggested Rabinovich.

Turkey could have a key role to play, having restored relations with Israel following Netanyahu's apology last week over the deaths of nine Turks in an Israeli crackdown on a Gaza-bound aid flotilla in 2010.

Kerry said at the weekend that the two countries' rapprochement was a vital factor in developing peace and stability in the Middle East.

And Turkish Prime Minister Recep Tayyip Erdogan's proposal to visit the Palestinian territories next month has met with only a muted response from Washington.

"As a more serious drive towards some kind of a peace process is being lead by the United States, people's real positions will be tested, including that of Hamas," Rabinovich said.

"There will be a point at which ambivalent statements won't work and one will be required to take a definitive stand and then we'll know."