Israel has warned thousands of people in the Rafah area on the Egyptian border to leave their houses ahead of planned air strikes.
"You have until 8am [06:00 GMT]," on Thursday, said leaflets which were dropped by the Israeli military.
Witnesses said a house and a suspected tunnel were hit in two air raids Rafah early on Thursday.
At least 700 Palestinians, including 219 children, have died in Gaza since Israel began its assault on December 27, and that number continues to climb. More than 3,080 people have also been wounded.
Seven Israeli soldiers and three civilians have died in the same period.
Soon after the three-hour lull on Wednesday, an Israeli air raid on a car in Beit Lahia, near Gaza's northern border with Israel, killed three children and their father, who was described as a civilian by medical workers in the besieged strip.
Palestinians and aid workers in and around Gaza City had used Wednesday's brief respite to recover dead bodies, treat the wounded, and gather much-needed supplies in and around Gaza City.
Peter Lerner, an Israeli military spokesman, announced "offensive" military action across the strip would be suspended for three hours every alternating day, although the timings may vary.
Despite this, Israeli air raids were reported on other parts of the Palestinian territory during Wednesday's announced timeframe of 1pm-4pm (11:00GMT).
Most of Wednesday's clashes occurred in northern Gaza, with explosions reported in Jabalya and Beit Lahia.
In Gaza City, four people were killed and seven injured outside a Mosque in the Sheik Radwan neighbourhood.
Two people were also killed earlier when the Zeitoun district was targeted from the air.
Further south, air raids hit the towns of Khan Younis and Rafah, where over 20 houses were destroyed.
No Israeli injuries have been reported on Wednesday after around eight rockets were fired from Gaza into southern Israel.
Israel is facing mounting pressure to agree a ceasefire after an attack on a school run by the United Nations Relief and Works Agency (Unrwa) in the northern town of Jabaliya on Tuesday left 43 Palestinians dead and around 100 wounded.
Doctors said all the dead were either people sheltering in the school or residents of the nearby Jabalya refugee camp.
Israel claims missiles were fired from the UN building and that their troops were simply returning fire.
Around 15,000 Palestinians have had to flee the fighting so far, but have found few safe havens, as Israel and Egypt continue to largely keep border crossings shut.
Heba, a Gaza resident and mother of two, told Al Jazeera there was no place left in Gaza that can be considered safe.
"What happened in the school was a hugely offensive and inhumane thing. We never expected that people who sought refuge in a UN building would be attacked and killed," she said.
While earlier attempts to agree a ceasefire resolution at the UN have so far floundered, a French-Egypt proposal appears to be gaining some support.
The deal, which could include stationing international monitors at the Egyptian-Gaza border, has received qualified backing from the US and support from Mahmoud Abbas, the Palestinian president and leader of Hamas-rival Fatah.