A. Israel should stop all hostilities in the Gaza Strip land, sea and air including incursions and targeting of individuals.

B. All Palestinian factions shall stop all hostilities from the Gaza Strip against Israel including rocket attacks and all attacks along the border.

C. Opening the crossings and facilitating the movements of people and transfer of goods and refraining from restricting residents’ free movements and targeting residents in border areas and procedures of implementation shall be dealt with after 24 hours from the start of the ceasefire.

D. Other matters as may be requested shall be addressed.

2: Implementation mechanisms:

A. Setting up the zero hour for the ceasefire understanding to enter into effect.

B. Egypt shall receive assurances from each party that the party commits to what was agreed upon.

C. Each party shall commit itself not to perform any acts that would breach this understanding. In case of any observations Egypt as the sponsor of this understanding shall be informed to follow up.

KHAN YUNIS, Gaza Strip — In the 12 years that he has lived here in the Abassam neighborhood adjacent to Gaza’s eastern border, Eyad Qudaih said, he had never ventured more than 20 yards east of his white stucco home because Israel said the area was off limits.

But on Friday morning, emboldened by the new cease-fire, he took his four young daughters 300 yards east, to the small plot of land where he dreams of growing wheat as his father once did.

“It was like someone who was hungry and had a big meal,” Mr. Qudaih said, shortly after touching the border fence for the first time. “Grilled sheep with nuts.”

But around 11 a.m., the moment was interrupted by the sound of gunfire. A spokesman for the Israeli military said soldiers had fired warning shots and then at the feet of some Palestinians who tried to cross the border fence into Israeli territory. Mr. Qudaih’s cousin Anwar Qudaih, 20, was killed, and nine others were wounded, Health Ministry officials here in Gaza said.

The episode, which happened at the same spot where an antitank missile fired by Palestinians hit an Israeli jeep, wounding four Israeli soldiers two weeks ago, did not fracture the truce that ended the recent fighting between Gaza and Israel. But it did showcase the confusion that remains over the cease-fire deal announced Wednesday in Cairo. While Hamas officials have been boasting about the concessions they say they have exacted from Israel, Israeli officials say nothing has been agreed upon beyond the immediate cessation of hostilities.

On Thursday, the Israeli defense minister, Ehud Barak, said dismissively that Hamas’s main achievement so far was getting a document that was typed rather than handwritten. In substance, Israelis said that they agreed to discuss the border and other issues, but that those talks had not yet begun — and there did not appear even to be a mechanism in place for starting.

But that was clearly not the understanding of the hundreds of Gazans who thought that they would have access to the so-called buffer zone, a 1,000-foot-wide strip of land along Gaza’s northern and eastern borders, that had for years been so tantalizingly close, and yet beyond reach. Palestinians flocked to the fence on Thursday and Friday because their leaders said the cease-fire eased what they call Israel’s “siege” on Gaza, including restrictions on movement in the so-called buffer zone, a 1,000-foot strip on Gaza’s eastern and northern borders.

Hamas leaders said that was but one of the quality-of-life improvements that they had won. They also told their people that Israel would ease the three-mile limit on how far fishermen can venture from the coastline and the passage of people and goods through border crossings.

But an Israeli government official said Friday that since no further talks had taken place, its policies had not changed.

Riad al-Malki, the Palestinian foreign minister, described Friday’s shooting as a clear violation of the agreement that was signed, telling reporters at an unrelated news conference in Rome, “I hope it will be the exception rather than the rule.”

Health Ministry officials in Gaza said Friday that the Palestinian death toll from the fighting had grown to 167, not including Mr. Qudaih, as several people died of the wounds they had sustained in Israeli airstrikes. Six Israelis, two of them soldiers, were killed during the eight days of escalated fighting.

That the killing on Friday did not incite other violence suggests that Hamas, the militant Islamic faction that won elections in 2006 and took full control in 2007, is not looking for reasons to return to battle. But Ahmed Yousef, a former adviser to the Hamas prime minister, said patience would be limited.

“Gradual steps should be taken to give the impression to the people we are no longer under siege,” said Mr. Yousef, who remains close to the Hamas leaders and now runs a research organization called House of Wisdom. “It might take some time, but this is what we’re going to achieve in the long run. As long as there is progress, I think the people will continue the cease-fire. If there is no progress, this will start again.”

The buffer zone was established in 2005, when Israel withdrew from the Gaza Strip, which it had occupied since the 1967 war. Human rights organizations say that Israel drops leaflets warning residents to stay out of the area, and that its security forces killed 213 Palestinians near the fence between September 2005 and September 2012, including 154 who were not taking part in hostilities, 17 of them children.

Critics say Israel has classified broad sections of border land as a “no-go zone” in which soldiers are allowed to open fire on anyone who enters, which military officials have strongly denied.

Witnesses, including Hamas police officers, said that about 2,000 people flooded this area of the buffer zone in celebration of the cease-fire on Thursday, and that as many as 500 returned Friday morning starting at 7. The Israeli military spokesman described it as a demonstration, but residents said people were just walking the fallow land their fathers and grandfathers once tilled. Some talked to the soldiers through the fence. They placed atop it a tall green Hamas flag and a smaller Palestinian one, a sight unimaginable here a few days — or a few years — before.

One police officer, speaking on the condition of anonymity, confirmed that some crossed over a portion of the fence downed by the recent attack on the Israeli jeep and stood on the Israeli side.

“In case you were wondering,” Lt. Col. Avital Leibovich, a spokeswoman for the military, wrote on her Twitter account as reports of the shooting emerged, “trying to breach Gaza fence in order to enter #Israel is breaking cease-fire. #IDF responding with warning shots.”

Eyad Qudaih, who lives in one of the few houses in the area, said that when he heard the shooting, “I took my girls and escaped.” By afternoon, his cousin was buried after a funeral procession featuring the flags of Hamas as well as the rival factions Fatah and Islamic Jihad, an echo of the post-conflict unity on display here at cease-fire celebrations on Thursday.

Sgt. Ahmed Mahmoud of the Hamas police said about 2,000 officers had fanned out along the borders on Friday starting at 9 a.m. “to maintain the security.” In blue camouflage suits and navy jackets, they carried wooden sticks but no guns, which he said was part of the buffer-zone arrangement with Israel.

“Within one hour of the shooting, we controlled the area and all the people were out,” Sergeant Mahmoud said. “Now we won’t let people go in.”

By 1 p.m., more than a dozen Hamas police officers were arrayed along the fence, closer than they have dared go in years. Perhaps 50 yards away, on the other side, an Israeli soldier stood behind the open door of his jeep.

The crowds were gone, but a few children ran more freely in the field than they had ever before, one carrying a Palestinian flag. Their parents and grandparents talked outside, contemplating the fence and whether they would indeed be free to approach it today, tomorrow, next week.