RAFAH, Palestinian Territories, Nov 2 (AFP) - Israel's military said on Thursday (Nov 2) its forces have surrounded Gaza City in the Hamas-run and densely populated Palestinian territory as they pressed their assault against the Islamist group.

The Ezzedine Al-Qassam Brigades, the military wing of Hamas, warned Israel that its invading soldiers would go home "in black bags".

Spokesman Abu Obeida said: "Gaza will be the curse of history for Israel."

The Hamas warning came after Israeli military spokesman Daniel Hagari said troops had completely surrounded Gaza City after days of expanding ground operations.

"Israeli soldiers have completed the encirclement of the city of Gaza, the centre of the Hamas terror organisation," Hagari told journalists.

"The concept of a ceasefire is not currently on the table at all," he added.

Amid growing fears of the conflict spreading, Israel and Hezbollah fighters in Lebanon exchanged fire after a salvo of rockets slammed into a northern Israel town.

The White House said United States President Joe Biden was calling for humanitarian pauses in the conflict that would involve a "temporary, localised" cessation of hostilities, well short of a general ceasefire.

Leaving on a new Middle East tour, Biden's Secretary of State Antony Blinken said "we are determined to deter any escalation" in the Israel-Hamas war.

"We will be talking about concrete steps that can and should be taken to minimise harm to men, women and children in Gaza," he told reporters.

Hundreds more foreigners and dual nationals managed to escape war-torn Gaza for Egypt on Thursday as Israel's forces bombarded and fought ground battles in the besieged territory where thousands of people have died.

A source at the Rafah border crossing told AFP it will open again on Friday, with more foreign nationals and wounded Palestinians expected to enter Egypt from the Gaza Strip.

Egypt said it eventually plans to help evacuate 7,000 foreigners through Rafah.

The health ministry in Cairo said 21 wounded Palestinians and "344 foreign nationals, including 72 children" passed through the Rafah border crossing on only the second day it has opened for people to leave Gaza in nearly four weeks of fighting.

A list of those approved to travel shows hundreds of US citizens and 50 Belgians along with smaller numbers from various European, Arab, Asian and African countries.

"There was no food, no water, no gas, nowhere to take shelter," said US passport holder Salma Shaath, 14, as she prepared to cross.

"People were going to hospitals to sleep, there are a lot of martyrs, there is no internet, no communications and no electricity. Our house was bombed ... so we came here to Rafah."

The evacuation marks a tiny proportion of the 2.4 million people trapped in Gaza under ferocious Israeli bombardment since Hamas launched their bloody cross-border attack into Israel on Oct 7.

Lebanon's Hezbollah said it attacked 19 Israeli positions along the border simultaneously on Thursday, ahead of a speech by its leader Hassan Nasrallah on the Israel-Hamas war.

The Israeli military said "warplanes and helicopters attacked in recent hours targets of the Hezbollah terror organisation in response to fire from Lebanese territory earlier today, together with attacks with artillery and tank fire".

Lebanon's official National News Agency said four people were killed and others wounded, and Hezbollah announced another of its fighters killed.

Thursday's deaths raised to 71 the number killed in Lebanon since the Israel-Hamas war began, according to an AFP tally.

In northern Gaza, ground fighting flared again overnight as Israeli troops battled Hamas.

Israeli army chief of staff Lieutenant General Herzi Halevi said troops were inside Gaza, besieging Gaza City and "deepening infiltration" of Hamas-held areas.

"Israeli soldiers are fighting face-to-face with a brutal enemy," he told reporters.

Hamas's assault on Oct 7, which Israel says claimed 1,400 lives, was the bloodiest in the country's 75-year-history.