"Once these objectives are achieved and are followed by very strict and credible international guarantees, we will leave Gaza, having created this new situation," said Dan Gillerman, a senior Israeli diplomat.
Hamas says it will only halt rocket fire in exchange for lifting the stifling blockade of Gaza, enforced by Israel and Egypt since the Hamas takeover in 2007.
Opening the borders without conditions would mean de facto recognition of the rule of Hamas, something Israel, Egypt and much of the international community are loathe to do. The Islamic militants are branded as a terrorist movement by many, and have refused to recognize Israel or commit to previous peace agreements.
Palestinian Foreign Minister Riad Malki, who represents the West Bank Palestinian Authority that is a rival to Hamas, suggested Monday that an international force would "observe and monitor" the Arab crossings and provide protection to Palestinians.
Israel's concept is tougher, authorizing international forces to destroy tunnels that Hamas has used to smuggle in large amounts of rockets and explosives since seizing control of Gaza from Palestinian President Mahmoud Abbas in June 2007.
Some 300 tunnels were running under the Gaza-Egypt border before the offensive began, the Israeli military says, and Israeli warplanes have bombed them in a series of strikes in the past 10 days, including dozens on Monday.
During a six-month truce that expired Dec. 19, Israel only allowed in a trickle of goods, increasing Hamas' frustration and willingness to call off the deal. Hamas fired repeated rocket barrages into southern Israel after the cease-fire lapsed, drawing the latest Israeli invasion.
Over the weekend, Secretary of State Condoleezza Rice spoke to 17 foreign leaders to discuss components of a cease-fire, including preventing smuggling and opening Gaza crossings, said spokesman Sean McCormack.
A Rice-brokered deal in 2005 between Abbas and Israel would likely form the basis for any new arrangement. Under that agreement, EU monitors were deployed at the Rafah terminal on the Gaza-Egypt border to prevent smuggling of weapons and militants, while Israel observed Palestinian-supervised border traffic from a distance, via closed-circuit TV.
The European Union is proposing that monitors return to the Rafah terminal, and says the mission could also be expanded to Israel's cargo and passenger crossings with Gaza, according to a European diplomat. He spoke on condition of anonymity because French President Nicolas Sarkozy was discussing truce ideas with Israeli and Palestinian leaders Monday.
Europe appears willing to contribute monitors in any number of scenarios.
These could include watching entrances and exits from Gaza, monitoring a cease-fire if all sides agree, and even acting as customs agents to police what is coming in and out of Gaza. "We'll go as far as possible," the European diplomat said. "Everything depends on whether the Israelis trust us. If they want us to go as far as playing a customs role, we will."
Turkey, Israel's closest Muslim ally, also expressed willingness to contribute monitors.
Still, a key sticking point is who would be deployed on the Gaza side of the border. Egypt says it will only open Rafah if Abbas' forces staff the crossing. Egypt, worried about Islamic fundamentalism at home, is trying to contain Hamas, which is backed by Iran and Syria.
Abbas, who is eager to gain a new foothold in the territory, was to fly to New York later Monday to lobby at the United Nations for reviving the 2005 deal, his aides said.
However, Hamas has been cool to the idea of letting Abbas back into Gaza. Similar proposals were raised in the past as part of failed power-sharing talks between the two bitter rivals.
It's also not clear what sort of role Israel is ready to give the militant group.
Egyptian Foreign Minister Ahmed Aboul Gheit said reviving talks between the rivals is key to any cease-fire. Hamas and Abbas have been at odds since Hamas won 2006 parliament elections, and they view each other with distrust and even hatred.
Israel, for its part, won't be satisfied with bringing back EU monitors who lack policing powers.
Israel has been disappointed by the performance of international peacekeepers deployed in southern Lebanon under a cease-fire that ended its 2006 war with Lebanese Hezbollah guerrillas. Israeli officials say Hezbollah has been amassing weapons, despite the presence of the observers.
As a result, Israeli Foreign Minister Tzipi Livni says international monitors on the Gaza border should be empowered to close tunnels used to smuggle weapons to Hamas from Egypt — broader powers than those apparently envisioned by Abbas and the Arabs.
Malki, Abbas' foreign minister, said there is broad Arab support for monitors at Gaza's crossings and the tunnels should be shut down, though he did not say who should be responsible.
"If you are talking about observers that will go and shut down tunnels, they are not really observers," Malki told reporters at U.N. headquarters in New York. "We are talking about observers that will observe and monitor the performance at the Arab crossings."
"Within this package, of course, the whole industry of tunnels should be really shut down and should be really closed, and this is really a part of the total objective," he added.
Danny Ayalon, a former Israeli ambassador to the U.S., said physical obstacles on the Gaza-Egypt border should also be considered. Ideas floated in the past include scaffolding or concrete poured deep into the ground, he said.