At least three mortars were fired from Gaza into southern Israel on Thursday morning about two hours into a temporary lull in hostilities to allow humanitarian supplies into the area.
The mortars fell in open areas, and no injuries were immediately reported, the Israeli military said.
Israel, which said it would honor the cease-fire but not sit idle if attacked, did not immediately respond.
In a separate incident, the Israel Defense Forces said a soldier was injured during an "operational activity" near southern Gaza. The IDF responded with mortar fire. This incident happened around 2 p.m. (5 a.m. MT) during the humanitarian cease-fire that expired at 3 p.m. (6 a.m. MT) Thursday.
Meanwhile, Palestinian Authority President Mahmoud Abbas and Arab League Secretary-General Nabil Al-Arabi were in Cairo for talks Thursday aimed at reaching a cease-fire agreement.
A high-level Israeli security delegation left Cairo on Thursday after discussions on a new Egyptian cease-fire proposal, state-run al-Ahram reported.
The United Nations requested Thursday's brief respite in the conflict. 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.
During the temporary cease-fire, 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 fix water pipelines.
There were no reported airstrikes once 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.
Talks in Cairo
Despite Hamas' decision Wednesday to reject an earlier Egyptian proposal and not participate in the Cairo talks, a senior Egyptian official told CNN that "the initiative is ongoing and we are in touch with all relevant parties."
The official mentioned the United States, Israel and the Palestinians, but he would not say specifically 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 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.
Egypt is playing a large role in the talks despite its distrust of Hamas.
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.
In addition to the two incidents during the cease-fire, Hamas' military wing said it fired five rockets at the Israeli city of Beer Sheeva just before the cease-fire began.
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. The IDF released video of what it said depicted militants emerging from the tunnel. An explosion from an Israeli airstrike follows.
"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 stop the killing permanently 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.
"The initiative is no longer acceptable, and there is no basis for the continuation of this initiative," Hamas spokesman Sami Abu Zhuri 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.