Israel launched at least 10 airstrikes in response to rocket and mortar fire from Gaza. One hit the backyard of a mosque and killed a 10-year-old boy, Palestinian officials said.
In Israel, two people were hurt by rocket fire, police said.
It is not clear if the renewed fighting will derail the Cairo talks, which are aimed at reaching a sustainable truce, or if Egyptian mediators can find a way to prevent further escalation.
Hamas officials said that even though they refused to extend the three-day cease-fire, they were willing to continue negotiations.
An Israeli government official, speaking on condition of anonymity in line with government regulations, said Israel would not conduct negotiations under fire and would protect its citizens by all means.
The Israeli delegation left Cairo on Friday morning, and it was not clear if it would return.
Within minutes after the temporary truce expired at 8 a.m. (0500 GMT), Gaza militants began firing rockets. By midday, 33 rockets had been fired. Twenty-six landed in Israel, three were intercepted and four fell short in Gaza, the army said.
Israel eventually responded with what the military said were strikes "across Gaza," without elaborating.
Police in Gaza said most of the strikes hit empty fields, but that one struck the backyard of the Nour al-Mohammadi Mosque in the Gaza City neighborhood of Sheik Radwan.
Gaza health official Ashraf al-Kidra said a 10-year-old boy was killed and five boys were wounded, one of them critically.
Police also reported fire from Israeli tanks on northern Gaza and from Israeli gunboats at the central area of the strip.
In Israel, the army said it was prohibiting gatherings of more than 1,000 people in Jerusalem, Tel Aviv and other areas within 80 kilometers (50 miles) of the Gaza border because of the rocket fire.
The resumption of violence cast doubt over the Cairo negotiations.
Both Israel and Hamas are under international pressure to reach a deal. As part of such an arrangement, Israel wants to see Hamas disarmed or prevented from re-arming, while Hamas demands Gaza's borders be opened. No progress was reported in all-night talks that ended before dawn Friday.
Hamas, which has seen its popularity boosted for confronting Israel, entered the Cairo talks from a point of military weakness after losing hundreds of fighters, two-thirds of its rockets arsenal and all of its attack tunnels.
With no definitive statement that it would return to open war, the group appeared to be keeping its options open while several smaller Gaza militant organizations claimed responsibility for Friday's rocket fire.
Israeli government spokesman Mark Regev blamed Gaza militants for breaking the cease-fire. "The cease-fire is over," Regev said. "They did that."
The three-day truce came after a month of Israel-Hamas fighting, the third cross-border confrontation in just over five years.
Israel launched an air campaign on the coastal territory on July 8, and nine days later, sent in ground troops to target rocket launchers and cross-border tunnels built by Hamas for attacks inside Israel.
Since then, Israeli strikes on Gaza killed nearly 1,900 Palestinians, wounded more than 9,000, devastated large areas along Gaza's border with Israel and displaced tens of thousands of people.
Sixty-seven people, all but three of them soldiers, were killed on the Israeli side, and Gaza militants fired thousands of rockets at Israel over the past month.
Israel said it was going after Hamas targets, including rocket launching sites and military tunnels, and carried out close to 5,000 strikes.
The U.N. said most of those killed in Gaza were civilians and that in dozens of cases, strikes hit family homes, killing multiple members of the same family at once. The Israeli military said initial estimates show at least 40 percent of those killed were fighters.
Previous rounds of Israel-Hamas fighting ended inconclusively, setting the stage for the next confrontation because underlying problems were not resolved, particularly the stifling border closure of Gaza.
Israel and Egypt imposed the blockade after the Hamas takeover of Gaza in 2007, and have since enforced it to varying degrees.
The closure led to widespread hardship in the Mediterranean seaside territory, home to 1.8 million people. Movement in and out of Gaza is limited, the economy has ground to a standstill and unemployment is over 50 percent.
Israel argues that it needs to keep Gaza's borders under a blockade as long as Hamas tries to smuggle weapons into Gaza or manufactures them there.
Hamas, in turn, has rejected Israel's demands that it disarm.
The militant group has said it is willing to hand over some power in Gaza to enable its long-time rival, Western-backed Palestinian President Mahmoud Abbas, to lead Gaza reconstruction efforts but that it would not give up its arsenal and control over thousands of armed men.
The Gaza war grew out of the killing of three Israeli teens in the West Bank in June. Israel blamed the killings on Hamas and launched a massive arrest campaign, rounding up hundreds of the group's members in the West Bank, as Hamas and other militants unleashed rocket fire from Gaza.
Daraghmeh reported from Cairo. Associated Press writers Ibrahim Barzak in Gaza City, and Daniel Estrin and Yousur Alhlou in Jerusalem contributed to this report.
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