Israeli airstrikes killed at least 31 people in Gaza on Tuesday, local medics said and fighting ramped up, as the Israeli military said it had been targeting command centres used by its Islamist militant foe Hamas.

Palestinian health officials said at least 13 people, including women and children, were killed in two Israeli strikes on two houses in Nuseirat, one of the enclave's eight historic refugee camps.

There has been no immediate comment by the Israeli army on the two strikes.

Another strike on a school sheltering displaced Palestinian families in the Tuffah neighbourhood of Gaza City killed at least seven people, medics added.

The Israeli military said in a statement the air strike targeted Hamas militants operating from a command centre embedded in a compound that had previously served as Al-Shejaia School.

It accused Hamas of using the civilian population and facilities for military purposes, which Hamas denies.

Later on Tuesday, two separate Israeli attacks killed five Palestinians in Rafah in the southern Gaza Strip and in the Zeitoun suburb of Gaza City, medics said.

In Khan Younis, in the south of the enclave, six Palestinians were killed in an Israeli air strike on a tent housing displaced people, medics said.

The armed wings of Hamas, the Islamic Jihad, and other smaller militant factions said in separate statements that their fighters attacked Israeli forces operating in several areas of Gaza with anti-tank rockets, mortar fire, and explosive devices.

The renewed surge in violence in Gaza comes as Israel began a ground operation in Lebanon, saying its paratroopers and commandos were engaged in intense fighting with Iran-backed Hezbollah. The conflict follows devastating Israeli airstrikes against Hezbollah's leadership.

The operation into Lebanon represents an escalation of the conflict in the Middle East between Israel and Iran-backed militants that threatens to suck in the U.S. and Iran.

Hezbollah began firing rockets into Israel almost a year ago, in support of its ally Hamas in the war in Gaza, which began after the militant group staged the deadliest assault in Israel's history on Oct. 7.

The assault, in which Israel says 1,200 people were killed and more than 250 taken hostage, triggered the war that has devastated Gaza, displacing most of its 2.3 million population and killing more than 41,600 people, according to Gaza health authorities.

Some Palestinians said they feared that Israel's shift in focus to Lebanon could prolong the conflict in Gaza, which marks its first anniversary next week.

"The eyes of the world now are on Lebanon while the occupation continues its killing in Gaza. We are afraid the war is going to go on for more months at least," said Samir Mohammed, 46, a father of five from Gaza City.

"It is all unclear now as Israel unleashes its force undeterred in Gaza, Yemen, Syria, Lebanon, and God knows where else in the future," he told Reuters via a chat app.