WASHINGTON -- An indefinite cease-fire agreement reached Tuesday between Israel and Hamas in Gaza "is an opportunity, not a certainty," US Secretary of State John Kerry said on Tuesday, throwing his "strong support" behind the agreement.

"We are approaching the next phase with our eyes wide open. We have been down this road before and we are all aware of the challenges ahead," Kerry said. "Today’s agreement comes after many hours and days of intensive discussions about how a sustainable ceasefire might provide the space and the opportunity to address long-term issues."

Kerry said that "certain bedrock outcomes" are minimal requirements for such a long-term solution, including a guarantee for Israel that terrorist attacks, rocket firings, and tunnel construction will cease, as well as the establishment of full economic and social opportunities for Palestinians, and the reconstruction of the Gaza Strip.

But speaking to reporters on Tuesday, State Department spokeswoman Jen Psaki said that the Secretary of State had no plans to restart the peace process in the near future.

Noting the amount of time remaining in Obama's presidency— roughly two and a half years— she said that such a process was possible, but not immediately on the agenda.

Psaki also addressed the cease-fire with cautious optimism, referring to the news as a welcome development.

The Israeli government has insisted on reserving the right to destroy any tunnels discovered burrowed into Israeli territory. Asked whether such a demand was reflected in the cease-fire, Psaki said that US support for that right had not changed, adding that Israel has said that all tunnels so far identified had been destroyed.

Despite the Egyptian announcement of the cease-fire, rocket alert sirens continued to be heard in Israel's southern communities after the truce's slated commencement at 7 p.m. An Israeli was killed by one of dozens of mortar shells fired at the Eshkol Regional Council just before the cease-fire was set to commence.

Senior diplomatic officials said that given the history of the last dozens truces, most of which were violated before they expired by Hamas, the IDF remained prepared for any eventuality.

The Egyptian proposal was very similar to the one that Israel accepted and Hamas rejected over a month ago, on July 15.

The general parameters of the cease-fire is that this one will not be limited in time, that Israel will allow humanitarian aid – under supervision – into Gaza to begin rebuilding, and that within a month both sides will raise other issues.

Israel will raise the demilitarization of the Gaza Strip, and the steps needed to ensure that Hamas does not re-arm, while Hamas will demand a seaport, airport, the opening of the border crossings, the release of prisoners freed in the Gilad Schalit deal and then re-arrested, and the transfer of money to pay Hamas salaries. A month ago these were Hamas’ demands for stopping the fighting, demands that Israel made clear were completely unrealistic.  

Herb Keinon contributed to this report.

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