Three mortar shells fired from Gaza hit southern Israel on Thursday, the army said, just over two hours after a humanitarian ceasefire took effect.
The shells struck in the region of Eshkol, which borders the southern Gaza Strip, the army told AFP, without giving further details.
Earlier, the Israeli army said it foiled an "infiltration" into southern Israel by Gaza militants, shortly before a humanitarian ceasefire with Hamas took effect.
"This morning our forces successfully foiled a terror attack," army spokesman Lieutenant Colonel Peter Lerner told journalists in a telephone briefing.
Thirteen militants emerged from a tunnel under the southern Gaza border, and were headed towards Sufa kibbutz, a small community just over a kilometre (mile) away, when they were spotted, Lerner said.
Israel forces killed at least one of the militants in an air raid, he said, leaving the rest scurrying back towards the tunnel.
There were no details of any other deaths or injuries, and there were no casualties on the Israeli side, Lerner said.
Hamas's armed wing, the Ezzedine al-Qassam Brigades, claimed in a statement that it was behind the "operation".
But it denied any of its members had been killed in an air strike, instead saying they had completed their "mission" at 4:00 am (0100 GMT) before retreating back to the tunnel.
It did not elaborate on the aim of the mission.
Earlier, Israel and Hamas agreed to a UN request to halt hostilities for five hours on humanitarian grounds, while efforts continue to broker a longer-term truce.
The sides announced the temporary lull in fighting across the Gaza border after an Israeli strike killed four children on a beach in the coastal strip on Wednesday.
Ahead of the pause, which just began, hostilities continued early on Thursday with Israel's air strikes, on the 10th day of its campaign, taking the toll to 226 killed and 1,678 wounded, Gaza medical services said.
A Gaza-based human rights group says over 80% of them were civilians.
Since July 8, militants have fired more than 1,200 rockets at Israel. They claimed their first Israeli life on Tuesday.
The army said early on Thursday that 82 rockets had hit Israel during the course of Wednesday and more than 30 were intercepted by Israel's missile defences.
Hamas had rejected initial Egyptian efforts for a full ceasefire, saying it had not been included in the discussions.
The Israeli army announced it would halt its bombardment of Gaza between 10:00 am and 3:00 pm (0700 to 1200 GMT) Thursday, following a UN request for a humanitarian truce.
Hamas later followed suit.Airstrike kills four children on Gaza beach
"The Palestinian factions agreed to accept the offer from the United Nations for a cooling-down on the ground for five hours starting from 10 in the morning," spokesman Sami Abu Zukhri told AFP.
Meanwhile, in Cairo, a Hamas official met Egyptian leaders and Palestinian president Mahmud Abbas arrived to join the diplomatic efforts.
US President Barack Obama on Wednesday backed Egypt's efforts to broker a ceasefire, offering Washington's full diplomatic support.
"Over the next 24 hours, we'll continue to stay in close contact with our friends and parties in the region, and we will use all of our diplomatic resources and relationships to support efforts of closing a deal on a ceasefire."
Obama said that while he and the world were "heartbroken" by the deaths of civilians in the Gaza Strip, US ally Israel had the "right to defend itself from rocket attacks that terrorise" its population.
The first strike scattered terrified children and adults on the beach. A second and third struck as they ran, setting fire to huts on the beach.
The strikes appeared to be the result of shelling by the Israeli navy against an area with small shacks used by fishermen.
Several children ran inside a hotel where at least three had shrapnel injuries.
Several hours after the strikes, the Israeli military described the deaths as "tragic" and said it was investigating the incident.
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"Based on preliminary results, the target of this strike was Hamas terrorist operatives," the military said in a statement.
"The reported civilian casualties from this strike are a tragic outcome."
The Israeli military dropped flyers and sent text messages Wednesday warning 100,000 people in northeastern Gaza to evacuate their homes ahead of an air campaign targeting "terror sites and operatives" in Zeitun and Shejaiya, two flashpoint districts east of Gaza City.
An identical message was sent to Beit Lahiya in the north.
But for patients at Al-Wafa hospital in Shejaiya, the warning simply provoked even more fear.
"There is no place safe in Gaza," director Basman Alashi told AFP, adding that most of his patients were completely incapacitated.
"If a hospital is not safe, where is?" he said as the sound of nearby shelling rattled the windows.
Hamas dismissed the warning as a scare tactic, telling residents there was "no need to worry."