The deal came into effect at dawn on June 19 and seemed to be holding until late Monday night, when a Palestinian mortar shell was fired into Israel. On Tuesday, several Qassam rockets landed in southern Israel, slightly injuring two people. Islamic Jihad claimed responsibility for the attack.
Despite the apparent violations, Hamas said it was committed to the cease-fire, and the rocket salvo elicited no immediate response from Israel.
Hamas is expecting the cease-fire to bring a letup in Israeli attacks and an easing of the Israeli blockade of Gaza, which was designed to weaken support for Hamas among the strip's 1.5 million, mostly aid-dependent Palestinians.
For Israel, the cease-fire is expected to bring a reprieve from Palestinian shelling and rocket attacks, though Tuesday's rocket attack fueled speculation that the quiet would not hold for long.
Palestinian rocket attacks have killed 16 people since 2004, including three in recent weeks, and raised the pressure on Prime Minister Ehud Olmert to order an invasion of Gaza.
The Gaza problem has presented the scandal-plagued prime minister with a thorny dilemma.
If Olmert were to order a major invasion, left-wingers would go after him, and the Israel Defense Forces could end up in the same insoluble quagmire it encountered in Lebanon in 2006 with Hezbollah. But by agreeing to a truce, the right-wing opposition has slammed Olmert for dealing, albeit indirectly, with Hamas, saying it will give Hamas time to rearm and enable the terrorist group to gain legitimacy abroad.
Some Israeli strategists suggest that the Olmert government may have to do both: Try out a truce, then invade Gaza if it fails.
"My feeling is that ultimately we are destined for violent confrontation" with Hamas, Deputy Defense Minister Matan Vilnai said last week during a visit to the Gaza-Israel border. "But before we send our boys to the battlefield, we have to know that we exhausted other options first."
Israeli Defense Minister Ehud Barak told France's Le Monde newspaper, "Historically, we are on a collision course with Hamas. But it still makes sense to grasp this opportunity."
Olmert was unapologetic last week about his agreeing to a cease-fire -- a decision backed by his security Cabinet -- and said Israel would resort to force if the cease-fire fails.
"The terrorist organizations that control the Gaza Strip have been under continuous military and economic pressure in recent months as a result of the government's policies. It was they who sought the calm," Olmert said in a speech on June 18, using Israel's more amorphous term for the truce. "I would like to emphasize and make it clear that we did not hold -- and I will not hold -- negotiations with any terrorist organization. We have no illusions."
Hamas, which found itself cut off in Gaza after seizing control of the territory from the Fatah faction of Palestinian Authority President Mahmoud Abbas last June, has demanded an end to Gaza's "siege."
Hamas' armed wing, which lost a gunman to an Israeli airstrike just hours before the truce began, also has said it is ready to resume attacks. The terrorist group has made no secret of its plan to use the quiet of the cease-fire to stockpile weapons and train fighters.
Hamas refuses to renounce its mission to overthrow the Jewish state, but its leader in Gaza, Ismail Haniyeh, the deposed P.A. prime minister, struck an unusually conciliatory note last week.
"Should Israel honor the calm, it will also provide some relief to the Israelis," Haniyeh told reporters.
Olmert flew to the Egyptian resort of Sharm el-Sheik this week for talks with Egyptian President Hosni Mubarak about staunching arms smuggling from the Egyptian Sinai to Gaza and stepping up efforts to secure a prisoner swap involving Israeli soldier Gilad Shalit, who was taken captive two years ago. He would be swapped for Palestinian terrorists jailed in Israel.
Shalit's father, Noam, told Israeli media he felt "cheated" by the government's willingness to enter a Gaza truce without a guarantee that his son would be returned.
But Israeli officials said Egypt has agreed to hold off on opening its border with Gaza -- a key Hamas demand -- until there is progress in talks on Shalit's return.
The IDF is expected to be ready for a last-resort invasion of Gaza, if the cease-fire fails.