JERUSALEM (Reuters) - Outgoing Israeli Prime Minister Ehud Olmert is mounting a last-ditch effort to free a captured Israeli soldier by blocking an Egyptian-brokered ceasefire in the Gaza Strip until Hamas agrees to release him.

Whether Olmert’s brinkmanship can produce a breakthrough in the few weeks he has left depends on Israel making difficult concessions that could bolster Hamas, and on the Islamist group taking a gamble on the Jewish state keeping its word. Many diplomats are skeptical all the pieces will fall in place.

Hamas has no faith that Israel, which is about to change governments, will abide by commitments under the proposed ceasefire, mainly to keep Gaza’s border crossings open, if captured soldier Gilad Shalit is freed.

Wary of taking steps it believes would bestow legitimacy on Hamas, Israel has refused to provide guarantees and has rebuffed a proposal for the U.N. to monitor the compliance of both sides, according to diplomats who spoke on condition of anonymity.

“We will not allow the opening of the crossings to Gaza ... certainly not before Gilad Shalit is back home,” Olmert said on Sunday, leaving Hamas with little to gain up front.

Hamas is counting on Egypt to ensure Israel’s compliance and the Islamist group may find it has little alternative. “Hamas understands Israel may not abide by its commitments after Shalit is freed,” a Palestinian official involved in the talks said.

But Hamas would at least have “a big achievement” in freeing long-serving prisoners in a swap for the soldier, captured in a cross-border raid by Gaza militants in 2006, the official added.

Israel believes last month’s military offensive in the Gaza Strip increased its leverage over the territory’s Hamas rulers.

The air, sea and land bombardment, which Israel launched with the declared aim of halting rocket attacks, killed more than 1,300 Palestinians, destroyed some 5,000 homes and decimated much of Gaza’s infrastructure, local officials said.

OPPORTUNITY

Many smuggling tunnels along Gaza’s border with Egypt were destroyed, crimping Hamas’s resupply lines. To rebuild, Gazans need Israel and Egypt to open the border crossings permanently.

“When are we going to get another window of opportunity like this?” asked an Israeli official, summing up Olmert’s thinking.

Tuesday’s inconclusive election in Israel has triggered what may be a protracted battle over who will get to form the next government, giving Olmert several weeks to maneuver.

Hamas has demanded the release of 1,400 Palestinian prisoners in exchange for Shalit. Western diplomats said Olmert would likely free closer to 1,000, including some Hamas militants involved in deadly attacks against Israelis.

“This is precisely the difficulty,” Internal Security Minister Avi Dichter said of choosing whom to release.

Ahead of a deal with Hamas, Israel was considering freeing Palestinian uprising leader Marwan Barghouthi to bolster President Mahmoud Abbas’s Fatah faction, Israeli officials and Channel 10 television reported.

Officials said Olmert planned to step up indirect negotiations with Hamas on a formula for a prisoner exchange, which would likely be carried out in stages. Defense official Amos Gilad planned to return to Egypt this week, diplomats said.

The question is whether Olmert can withstand international pressure to open the crossings more broadly if a Shalit deal is not reached, and whether U.S. President Barack Obama intervenes.

Obama’s Middle East envoy, George Mitchell, plans to return to the region next week, followed by Secretary of State Hillary Clinton a week later, diplomats said. During his last visit, Mitchell urged Olmert to ease Gaza’s closure, to no avail.

Diplomats said the Obama administration could try to break the stalemate by joining the European Union in insisting on guarantees the crossings will remain open, a key Hamas demand.

The Obama administration supports Abbas in his power struggle with Iranian-backed Hamas for control of Gaza’s gateways to the outside world.

But Israel asserts that opening the border crossings fully would only strengthen Hamas, which won a 2006 Palestinian election and forcefully seized control of the enclave 18 months later after routing Abbas’s secular Fatah forces there.

“The problem is that none of them trusts each other,” a senior Western diplomat said.

Hamas does not want to give Abbas a foothold that he could use to get credit for rebuilding. Israel has also insisted on retaining the right to reseal the border for “security” reasons.

“Why would Hamas believe Israel?” asked a senior European diplomat, pointing to a previous Egyptian-brokered ceasefire.

Under that six-month deal, Israel was supposed to let 30 percent more goods into the Gaza Strip. Citing Israel’s failure to do so, Hamas pulled out of the deal and renewed cross-border rocket fire, triggering last month’s war.