At least three mortars were fired from Gaza into southern Israel on Thursday morning, some two hours after a temporary lull in hostilities went into effect to allow humanitarian supplies into the area.
The mortars fell in open areas and no injuries were immediately reported, the Israeli military said. Mortars are smaller and have a more limited range than rockets.
Israel, which said it would honor the cease-fire but not sit idle if attacked, did not immediately respond.
The five-hour long temporary halt in fighting went into effect at 3 a.m. ET, requested by the United Nations to offer a brief respite in a conflict that has killed more than 220 people.
Banks opened for the first time in 10 days in Gaza and residents poured into the streets.
Red Cross officials visited hospitals and damaged houses to assess medical needs, and worked with local officials to quickly fix water pipelines, which has left hundreds of thousands without water.
There were no reported air strikes since the cease-fire began. Still, the fear of death hung heavily over Gaza. The health ministry warned civilians to avoid gathering in squares.
"Should the humanitarian window be exploited by Hamas or other terror organizations for the purpose of launching attacks against Israeli civilian or military targets the IDF will respond firmly and decisively," the Israeli military said.
Shortly before the cease-fire's start, Hamas's military wing said it fired five rockets at the city of Beer Sheeva. And the Israeli military said it foiled an attempt by 13 Hamas militants who tried to enter the southern Israeli community of Sufa through a tunnel.
"We were sitting at home while we heard the sounds of gunfire and bombardments from behind our house. Later on, all residents were informed that it was an infiltration attempt," said Eyal Brandeis, the director of the Sufa kibbutz.
"Our community is now back to its routine. I think routine is the best way to keep your sanity."
A rejected deal
On Tuesday, an effort to permanently stop more than a week of killing stalled when Israel resumed airstrikes following a brief, one-sided cease-fire brokered by Egypt. While Israel paused for six hours, Hamas leaders rejected the deal and continued firing rockets.
They said they had not been consulted, and complained the deal did not address their demands for greater freedom for Gaza's 1.8 million residents.
"The initiative is no longer acceptable, and there is no basis for the continuation of this initiative," Hamas spokesman Zhuri had told CNN.
Deaths on Gaza beach
Anger is rising over civilian deaths -- including those of four children killed while playing on the beach.
The boys, ages 9 to 11, died Wednesday when a shell from an Israeli gunship exploded near them on a beach near Gaza City, according to Palestinian officials.
Their names were Ismail, Zakaria, Ahed and Mohamed -- all of them cousins from the extended Bakr family.
An Israeli official said the shelling was another example of Hamas using civilians as human shields -- intimating that the boys had been left to play near a rocket launcher.
"What they are deliberately doing is seeking to kill as many Palestinians as possible in order to yell to the world to, 'Help us,' " Israeli Cabinet member Naftali Bennett told CNN. "This is cynical and this is cowardly."
A Hamas official, however, called the shelling by an Israeli gunship a "massacre" and a "war crime" and demanded U.N. action.
"Those children were not firing rockets, they were just playing," Hamas spokesman Zhuri told reporters.
Hundreds of people gathered for the boys' funeral Wednesday, where there were angry chants and deep grief.
"I felt as if the world had come to an end when I heard the news," said Ramiz Bakr, the blind father of 11-year-old Mohamed. "I wish I had died before hearing he was dead."
Israel's military said it was aware of the deaths and was investigating. The military never intentionally targets civilians, said spokesman Brig. Gen. Moti Almoz.
"Based on preliminary results, the target of this strike was Hamas terrorist operatives. The reported civilian causalities from this strike are a tragic outcome," the IDF said in a statement.
The event inflamed already raw emotions over civilian deaths in Gaza, where at least 230 Palestinians have been killed and close to 1,700 have been injured since Israel began its anti-Hamas military operation July 7, according to Palestinian health officials.
The one fatality on the Israeli side occurred Monday when a mortar shell hit a man at the Erez border crossing, Israeli Rescue Services said.
Talks in Cairo
Diplomats continued Thursday to try to find a more lasting halt to the violence.
A senior Egyptian official told CNN that an Israeli delegation is in Cairo to discuss proposals for a cease-fire in Gaza.
"The initiative is ongoing and we are in touch with all relevant parties," the official said, mentioning the United States, Israel and the Palestinians. But he would not say specifically that Hamas was involved.
"We hope the Palestinian leaders will accept the initiative for the sake of the protection of the Palestinian people," the Egyptian official said. "We urge them to stop fire immediately and accept the initiative to avoid further bloodshed."
Hamas had declined to join talks Wednesday in Cairo between Egyptian President Abdel Fattah el-Sisi and Palestinian Authority President Mahmoud Abbas.
Like Israel, Egypt considers Hamas a terror organization because of the group's roots in the Muslim Brotherhood, which Egypt's military-led government banned after the country's 2013 coup.
Hamas officials have said they are not opposed to a cease-fire, but want to see a broad agreement that would, among other things, end restrictions on border crossings that they say are choking the life out of Gaza's 1.8 million residents.
"I think what they want is to see a cease-fire agreement that addresses the real problems that they face and the system of violence that is this siege, that is the occupation, so that it can be a genuine cease-fire agreement that brings an end to hostilities, not just from one side," Yousef Munayyer, executive director of the Palestine Center, a pro-Palestinian think tank, told CNN's "New Day."
But Israeli Prime Minister Benjamin Netanyahu said that Hamas had brought the continued Israeli operation on itself after rejecting the Egyptian-brokered cease-fire.
"We held our fire for six hours and during that time, Hamas continued to barrage our cities with rockets," Netanyahu said. "Hamas thus shut the door to a diplomatic solution, and it therefore bears sole the responsibility for the continuation of the violence."