Israeli airstrikes killed at least 37 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, Reuters reported.

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.

Hours later, an Israeli airstrike on a car in western Khan Younis, killed six Palestinians, medics said. Footage circulated on social media, which Reuters could not immediately authenticate, showed a mangled, burnt-out vehicle, read the report.

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.

Israel's widely expected ground invasion of Lebanon appeared to be getting underway early on Tuesday as its military said troops had begun "limited" raids against Hezbollah targets in the border area, Reuters reported.

The military said in a statement that it had begun "limited, localised, and targeted ground raids based on precise intelligence" against Hezbollah in southern Lebanon villages close to the border that posed "an immediate threat to Israeli communities in northern Israel".

It said the air force and artillery were supporting the ground forces with "precise strikes."

Local residents in the Lebanese border town of Aita al-Shaab reported heavy shelling and the sound of helicopters and drones overhead. Flares were repeatedly launched over the Lebanese border town of Rmeish, lighting up the night sky.

On Monday, Israeli Defence Minister Yoav Gallant had told local council heads in northern Israel that the next phase of the war along Lebanon's southern border would begin soon, and would support the aim of bringing home Israelis who have fled Hezbollah rockets during nearly a year of border warfare.

The ground invasion represents an escalating conflict in the Middle East between Israel and Iran-backed militants, sparked by an assault on Israel by Palestinian militant group Hamas on Oct. 7, 2023, that now threatens to suck in the U.S. and Iran, read the report.

An Israeli strike in Lebanon early on Tuesday targeted Mounir Maqdah, commander of the Lebanese branch of the Palestinian Fatah movement's military wing, the Al-Aqsa Martyrs Brigade, according to two Palestinian security officials.

His fate was unknown.

The strike hit a building in the crowded Ain al-Hilweh Palestinian refugee camp near the southern city of Sidon, the sources said. It marked the first strike on the camp, Lebanon's largest Palestinian camp, since cross-border hostilities between Hezbollah and Israel broke out nearly a year ago.

In Syria, three civilians were killed and nine others injured in an Israeli airstrike on the capital Damascus, Syrian state media said on Tuesday citing a military source. Israel's military said it does not comment on foreign media reports.

Israel has been carrying out strikes against Iran-linked targets in Syria for years but has ramped up raids since the Hamas attack on Israel's southern territory on Oct. 7, 2023.

Hamas killed 1,200 people and took about 250 hostage in its assault on Israel, according to Israeli tallies. Israel in response launched a massive assault on Hamas in Gaza, reducing most of the Palestinian territory to rubble, displacing most of its 2.3 million people and killing more than 41,300 Palestinians, according to the Gaza health ministry.

Israel's ground invasion into Lebanon follows its deadly detonation of booby-trapped Hezbollah pagers, two weeks of airstrikes, and its killing on Friday of Hezbollah head Hassan Nasrallah, which dealt the group one of the heaviest blows in decades, Reuters reported.

The intensive air strikes have eliminated several Hezbollah commanders but also killed about 1,000 civilians and forced one million to flee their homes, according to the Lebanese government.

Overnight, strikes hit Beirut's southern suburbs, a security source said. A Reuters reporter witnessed a flash of light and a series of loud blasts about an hour after the Israeli military warned residents to evacuate areas near buildings it said contained Hezbollah infrastructure south of the Lebanese capital.

In the past 24 hours, at least 95 people had been killed and 172 wounded in Israeli strikes on Lebanon's southern regions, the eastern Bekaa Valley, and Beirut, Lebanon's health ministry said early on Tuesday.

Hezbollah's deputy leader Naim Qassem, in a first public speech on Monday since Nasrallah's death, said that "the resistance forces are ready for a ground engagement."

He said Hezbollah had continued to fire rockets as deep as 150 km (93 miles) into Israeli territory.

"We know that the battle may be long. We will win as we won in the liberation of 2006," he said, referring to the last big conflict between the two foes.

Late on Monday, Lebanese troops pulled back about five kilometres (3 miles) from positions along Lebanon's southern border with Israel, a Lebanese security source told Reuters. A Lebanese army spokesperson did not confirm or deny the movement.

Lebanon's army has historically stayed on the sidelines of major conflicts with Israel, and in the last year of hostilities has not fired on the Israeli military, read the report.

The White House and the U.S. State Department did not immediately respond to a request for comment on Israel's ground operations in Lebanon.

But on Monday, U.S. President Joe Biden had called for a ceasefire.

"I'm more worried than you might know and I'm comfortable with them stopping," Biden told reporters when asked if he was comfortable with Israeli plans for a cross-border incursion. "We should have a ceasefire now."

Israel last week rejected a proposal by the U.S. and France calling for a 21-day ceasefire on the Lebanon border to give time for a diplomatic settlement that would allow displaced civilians on both sides to return home.

Palestinian militant group Hamas said an Israeli strike killed its leader in Lebanon on Monday, while another Palestinian militant group said three of its leaders were killed in a strike on Beirut, the first attack within the city limits.

Hamas said its leader in Lebanon, Fateh Sherif Abu el-Amin was killed, along with his wife, son, and daughter, in a strike that targeted their house in a Palestinian refugee camp in the southern city of Tyre in the early hours of Monday.

As Israel escalates hostilities against Iran's allies in the region, the Popular Front for the Liberation of Palestine (PFLP) said three of its leaders were killed in a strike that targeted Beirut's Kola district.

The strike hit the upper floor of an apartment building, Reuters witnesses said.

There was no immediate comment from Israel's military.

Israel's increasing frequency of attacks against the Hezbollah militia in Lebanon and the Houthi militia in Yemen have prompted fears that Middle East fighting could spin out of control and draw in Iran and the United States, Israel's main ally.

The PFLP is another militant group taking part in the fight against Israel.

Israel on Sunday launched airstrikes against the Houthi militia in Yemen and dozens of Hezbollah targets throughout Lebanon after earlier killing the Hezbollah leader.Lebanon's Health Ministry has said more than 1,000 Lebanese have been killed and 6,000 wounded in the past two weeks, without saying how many were civilians.

The government said a million people - a fifth of the population - have fled their homes.

The intensifying Israeli bombardment over two weeks has killed a string of top Hezbollah officials, including its leader Sayyed Hassan Nasrallah.

Israel has vowed to keep up the assault and says it wants to make its northern areas secure again for residents who have been forced to flee Hezbollah rocket attacks.

Israeli drones hovered over Beirut for much of Sunday, with the loud blasts of new airstrikes echoing around the Lebanese capital.