CAIRO, Egypt — Israel and the Islamic terrorist group Hamas have agreed on a truce to begin Thursday, Egypt’s state-owned news agency said today.

A Hamas official in Gaza, speaking on condition of anonymity because he is not authorized to release the information, confirmed the truce.

Israeli officials declined to confirm a deal, but said Israel’s negotiator in the truce talks was rushing to Cairo and that they were “cautiously optimistic.”

Egypt’s MENA agency cited an unnamed high-level Egyptian official as saying that both sides “have agreed on the first phase” of an Egyptian package to end the violence at the Gaza Strip.

The first phase is a “mutual and simultaneous calm” that will start at 6 a.m. Thursday, MENA said.

The agreement is designed to end months of daily Palestinian Arab rocket and mortar assaults on Israeli border towns and bruising Israeli retaliation. Egypt has been laboring for months to broker an agreement between Israel and Hamas, which do not have direct contact with each other.

Gaza terrorists have been bombarding southern Israel with rockets and mortars for seven years. The rate of fire increased after Israel pulled its troops and settlers out of Gaza in 2005 and stepped up further last year after Hamas wrested power from forces loyal to the president of the Palestinian Authority, Mahmoud Abbas.

Israel has responded with pinpoint air and ground attacks that have killed hundreds of Palestinian Arabs, many of them civilians. It has also imposed a strict blockade on Gaza, letting in only limited amounts of humanitarian aid, restricting fuel supplies, and widening already rampant unemployment. Ending the economic sanctions by opening Gaza’s crossings with Israel and Egypt has been a major Hamas demand in the cease-fire talks.

Although the Rafah crossing lies on the Gaza-Egypt border, Europeans monitoring the passage require Israeli security clearance to operate. That clearance has not been given since Hamas took over Gaza.

Much skepticism has surrounded the talks, and not only because past accords — most recently, a November 2006 deal — have broken down fairly quickly.

Israel is suspicious of Hamas’ motives, especially since the terrorist group has declared it would take advantage of any lull to rearm. Israel also is reluctant to legitimize Hamas’ rule in Gaza through a truce agreement. Hamas rejects the existence of a Jewish state and has killed more than 250 Israelis in suicide bombings.

But with the Israeli government under heavy domestic pressure to halt the rocket fire, the choices were a truce or a broad invasion of Gaza. Last week, Israeli leaders decided to put off a large-scale military campaign to give truce efforts more time to succeed.

Previous large-scale offensives have failed to halt the terrorist attacks. An even wider operation designed to overthrow Gaza’s Hamas regime would mean house-to-house fighting in one of the world’s most crowded territories, virtually guaranteeing high casualties.