Israeli soldiers have launched several small-scale ground incursions into Gaza, clashing with Hamas fighters during raids into the besieged Palestinian enclave where the death toll has passed 5,000 and civilians are trapped in harrowing conditions amid relentless aerial bombardment.

Gaza's health ministry said 436 people had been killed in bombardments over the past 24 hours, most of them in the south of the narrow, densely populated territory. With the territory's 2.3 million people running short of basics, European leaders looked set to follow the United Nations and Arab nations in calling for a "humanitarian pause" in hostilities so aid could reach them.

As Israeli troops and tanks mass on the Israeli-Gaza border, readying to launch a much-publicized incursion into the tiny Palestinian enclave, the EU's top diplomat Josep Borrell said that a pause in Gaza military operations would mean a temporary interruption of military activity and was "a less ambitious demand" than a proper ceasefire.

READ MORE:

Gazans running out of places to shelter, says UN

Gaza healthcare system on 'verge of complete collapse' – UK surgeon

Israel delayed by logistics, politics and the 'Gaza Metro' – expert

Meanwhile, the conflict is escalating beyond Gaza, as Israeli aircraft also hit positions in south Lebanon held by Hezbollah, which, like Hamas, is a group allied to Israel's regional foe Iran. Almost 20,000 people have been internally displaced in south Lebanon and elsewhere since early October due to the tensions building at the Lebanese-Israeli border, a UN agency said on Monday.

Two U.S. officials said that American troops in Syria were targeted by drones but there were no injuries, the latest in a series of attacks against U.S. forces in the Middle East. The officials, speaking on condition of anonymity, said the attack took place at Al-Tanf base, near Syria's borders with Iraq and Jordan. When grilled on the attacks, the Pentagon said it had not seen a direct order from Iran – a regional ally of Hamas – to attack U.S. troops in the region.

Israeli forces also killed several Palestinians in clashes in the occupied West Bank, while Hamas said it had fired rockets into Israel in response to the alleged targeting of Palestinian civilians. The UN said desperate Gazans lacked food, water, medicines and places to shelter from the unrelenting pounding that has flattened swathes of the enclave. Some aid was trickling over one border crossing into Gaza, but only a small fraction of the amount needed.

At least 5,087 Palestinians have been killed in two weeks of strikes, including 2,055 children, the health ministry said.

The Israeli bombardment was triggered by an October 7 cross-border assault on Israeli communities by Hamas fighters who killed 1,400 people and took more than 200 hostage - the deadliest attack on Israelis in a single day since the state of was founded 75 years ago.

Fighting inside Gaza

Both Israel and Hamas reported overnight clashes in Gaza. Israel said ground forces mounted limited raids to fight Hamas and that air strikes focused on sites where Palestinian fighters were assembling to respond to any wider Israeli invasion.

"These raids are raids that kill squads of terrorists who are preparing for our next stage in the war. These are raids that go deep," military spokesperson Daniel Hagari said, adding that the operations also sought information on the 222 hostages held by Hamas.

Hamas's armed wing, the Izz el-Deen al-Qassam Brigades, said its fighters engaged with an Israeli force that infiltrated southern Gaza, destroying two bulldozers and a tank and forcing the raiders to withdraw. One Israeli soldier was killed during a raid, the Israeli military said, but it did not acknowledge the destruction of any military equipment. The Al-Qassam Brigades also said they were firing missiles at the southern Israeli towns of Ashkelon and Mavki'im in response to the Israeli targeting of civilians in Gaza.

The UN humanitarian office (OCHA) said about 1.4 million of Gaza's population – more than half – were now internally displaced, with many seeking refuge in overcrowded U.N. emergency shelters. Israel has ordered Gaza residents to evacuate the north. But many who had fled appeared to be returning north due to increased bombardments in the south and lack of shelter.

"They told us to evacuate your place and go to Khan Younis because it is safe... They betrayed us and bombed us," said 18-year-old Dima Al-Lamdani who lost her parents, seven siblings and four members of her uncle's family in an air strike after the family moved south.

A third convoy of aid entered the Rafah crossing from Egypt on Monday, adding to 34 trucks in the previous two days. The U.N. said aid arriving so far was just 4 percent of the daily average before the hostilities.

In Brussels, EU leaders meeting later this week will call for a ceasefire to allow aid to flow safely, according to draft conclusions. They said they backed a similar call from UN Secretary-General Antonio Guterres, who visited Rafah last week. Arab nations also want a truce.

Families of Israeli hostages dilemma

As Israel prepares to attack the Gaza Strip, many families of hostages seized by Hamas are pleading with the government to rein in the war effort and instead negotiate the release of their loved ones. Highlighting the appalling dilemma facing the whole country, other relatives warn mediation could take years and say their best hope lies with the military, hoping ground forces could find the missing men, women and children before it is too late.

Hamas fighters grabbed an estimated 222 people aged from nine months to 85 years during their attack earlier in the month. Many of those taken hold dual nationality, including many with U.S. and European passports. The hostages are believed to be hidden in the Gaza Strip.

Prime Minister Benjamin Netanyahu has vowed to eliminate Hamas and Israeli troops could enter Gaza at any moment, but many families are urging him to focus solely on the hostages. "This should be the top priority, not to destroy Hamas, not to control Gaza and not anything else," said Noam Alon, the boyfriend of Inbar Haiman, a 27-year-old artist who was one of dozens abducted from a music festival.

Family support groups are holding daily protests outside Netanyahu's office in Tel Aviv to keep the fate of the captives in the spotlight, and have set up a table with a place setting for each missing person in a city center square as a symbol of the plight of those abducted. On Sunday, President Isaac Herzog met scores of affected relatives at his Jerusalem residence, while outside, hundreds demonstrated calling for more to be done for the hostages.

"Revenge is not a plan," read one banner held up by Carmel Gorni, a political activist whose cousin, Yiftah Gorni, was killed during the Hamas assault. "We need to talk to Hamas. We can't always resort to war. We have so many Palestinian prisoners we can swap for our people," Gorni said. "If our soldiers go in, many people will die, including the hostages."

Not all the families agree. Ilan and Sandy Feldman, whose sister and brother-in-law Aviva and Keith Siegel were kidnapped, expressed doubts over whether the Siegels would survive prolonged captivity and thought an invasion was inevitable. "There is a sense that they won't come out alive. But I think this is bigger than me or us."

Jonathan Dekel-Chen, whose 35-year-old son Sagui was believed to have been kidnapped from a kibbutz, said Hamas had to be dealt with "now," but thought the army had to make rescuing the hostages the priority of any military campaign. "It is possible to do two things at once, even for this Israeli government, to do everything in its power to protect the lives and well-being of our loved ones while doing what it has to do to Hamas," he said.

Subscribe to Storyboard: A weekly newsletter bringing you the best of CGTN every