Strikes by air and shelling from tanks on the ground were also reported in central and southern areas of the Gaza Strip in what residents said late on Tuesday were almost 24 hours of non-stop bombardments.
In a post on social media platform X, Israeli army spokesperson Avichay Adraee urged residents of four zones in Beit Lahiya on Gaza's northern edge to move to two designated areas.
He said the military "will work with extreme force against terrorist infrastructure and subversive elements" in the region.
In a statement issued later on Tuesday, the military said it "follows international law and takes feasible precautions to mitigate civilian harm."
The renewed shelling and bombing of northern Gaza comes almost four months after the Israeli army announced it was drawing down troops there, saying Hamas no longer controlled those areas.
This month, Israel also drew down most of its forces in southern Gaza. But efforts to reach a ceasefire have failed, and Israeli bombardment and raids on territory where its troops have withdrawn are making it difficult for displaced Gazans to return to abandoned homes.
Tuesday's bombardment came after incoming rocket alerts sounded in two southern Israeli border towns, although no casualties were reported.
The armed wing of Islamic Jihad, a group allied to Hamas, claimed responsibility for the attacks on Sderot and Nir Am, indicating fighters were still able to launch rockets almost 200 days into the war, which has flattened large swathes of the enclave and displaced almost all of its 2.3 million people.
Hamas said Israel had achieved only "humiliation and defeat" with its offensive.
Speaking in a video aired by Al Jazeera television, Abu Ubaida, the spokesperson for Hamas' armed wing, called for an escalation in conflict across all fronts and praised Iran for its first direct attack against Israel earlier this month.
He also said Hamas was sticking to its demands in ceasefire talks for Israel to permanently end its war, pull all its troops from Gaza and allow the displaced to return to the north.
Israel has resisted a permanent ceasefire, saying that would only allow Hamas to regroup.
FAMINE RISKS
The U.S. special regional envoy for humanitarian issues, David Satterfield, told reporters in Washington that Gaza faces a high risk of famine, especially in the north. He urged Israel to get aid to those in need.
Philippe Lazzarini, head of the U.N. aid agency UNRWA, said the number of aid trucks entering Gaza reached 310, the highest daily total since the war began.
"This shows that when there is a will there is a way," he wrote on social media site X. "Famine in northern Gaza can be averted only through meaningful & uninterrupted supply including through @UNRWA."
Thick black smoke could be seen rising in northern Gaza from across the southern Israeli border. Shelling was intense east of Beit Hanoun and Jabalia and continued in areas such as Zeitoun, one of Gaza City's oldest suburbs, with residents reporting at least 10 strikes in a matter of seconds along the main road.
"The bombing from tanks and planes didn't stop," said Um Mohammad, 53, a mother of six living 700 metres from Zeitoun.
"I had to gather with my children and my sisters who came to shelter with me in one place and pray for our lives as the house kept shaking," she told Reuters via a chat app.
Just west of Beit Hanoun in Beit Lahiya, an air strike hit a mosque, killing a boy and injuring several others, while a medic was killed in shelling near the town stadium, medics said.
Elsewhere in the enclave, shelling hit the east of the main southern city Khan Younis a day after Israeli tanks raided the area.
In the Al-Nusseirat refugee camp in central Gaza, an Israeli airstrike killed four people late on Tuesday, medics said. Two people died in another strike on a house east of Rafah at the southern end of the Gaza Strip, they said.
Israel says it is seeking to eradicate Hamas, which controls the enclave, following an attack by the group on Oct. 7 killing 1,200 and taking 253 hostages by Israeli tallies.
Palestinian health authorities say more than 34,000 people have been confirmed killed in the seven-month war, with thousands more bodies unrecovered.
In Nasser Hospital, southern Gaza's main health facility, authorities recovered a further 35 bodies in the past day from what they say is one of at least three mass graves found at the site, taking the total found there to 310 in the past week.
Palestinians say Israeli troops buried corpses there with bulldozers to cover up crimes. The Israeli military said its troops dug up some bodies at the site and reburied them after testing to make sure no hostages were among them.
Israel says it was forced to battle inside hospitals because Hamas fighters operated there, which medical staff and Hamas deny.
