Nearly two weeks since Israel defied international opposition and sent troops into Rafah, which the army has described as the last Hamas stronghold, the UN said more than 810,000 Palestinians have fled the city.
"The question that haunts us is where will we go" said Rafah resident Sarhan Abu al-Saeed, 46.
"Certain death is chasing us from all directions," he said.
Witnesses told AFP that Israeli naval forces struck Rafah, and medics reported an air strike that hit a residential building in the city's western parts.
The army said Israeli troops were "conducting targeted raids on terrorist infrastructure" in eastern Rafah where they had found "dozens of tunnel shafts".
Since the start of the long-threatened Rafah incursion in early May, Israeli forces have also been engaged in intense fighting in northern and central Gaza where the army says Hamas has regrouped after previously announcing these areas cleared of militants.
An AFP correspondent and Palestinian medics said Israeli warplanes carried out overnight strikes on Gaza City's centre and the southern neighbourhoods of Zeitun and Sabra.
Witnesses also reported helicopters hovering over northern Gaza's Jabalia refugee camp, one of the areas that has seen a resurgence of fighting in recent weeks, and air strikes on Al-Bureij camp and Deir al-Balah in central Gaza.
Post-war 'strategy'
Israel's Prime Minister Benjamin Netanyahu has vowed to keep fighting Hamas in Gaza, following its October 7 attack that sparked the war, until the Iran-backed Islamist group is defeated and all remaining hostages are released.
Defence Minister Yoav Gallant -- who last week slammed the premier for not announcing post-war plans -- said Monday he told visiting US National Security Advisor Jake Sullivan of "Israel's duty to expand the ground operation in Rafah, to dismantle Hamas and to return the hostages".
Sullivan met with Netanyahu on Sunday and told him Israel must link the military operation against Hamas with a "political strategy" for Gaza's future, the White House said.
It added they also discussed the "potential" of a normalisation deal between Israel and Saudi Arabia, where Sullivan held talks before arriving in Israel.
The war broke out after Hamas's unprecedented October 7 attack on Israel, which resulted in the deaths of more than 1,170 people, mostly civilians, according to an AFP tally based on Israeli official figures.
Hamas also took about 250 hostages during the October 7 attack, of whom 124 remain held in Gaza including 37 the army says are dead.
Israel's retaliatory offensive against Hamas has killed at least 35,456 people in Gaza, also mostly civilians, according to data provided by the Hamas-run territory's health ministry.
Washington has pushed for a post-war plan for Gaza involving Palestinians and supported by regional powers, as well as for a broader diplomatic deal under which Israel and regional powerhouse Saudi Arabia would normalise relations.
Israel's centrist politician Benny Gantz has threatened to quit the governing hard-right coalition over just this issue if Netanyahu does not approve a post-war "action plan" by June 8.
Hamas lauds Raisi 'support'
Hamas, backed by Iran, expressed its condolences after Tehran had confirmed president Ebrahim Raisi died in a helicopter crash.
The Palestinian group said it appreciated Raisi's "support for the Palestinian resistance and tireless efforts in solidarity" with Palestinians since the start of Gaza war.
Israel has imposed a siege on the long-blockaded Gaza Strip, depriving its 2.4 million people of normal access to clean water, food, medicines and fuel, the suffering eased only by sporadic aid shipments by land, air and sea.
Truck arrivals have slowed after the Rafah crossing with Egypt closed when Israel launched its operation in the city.
After a series of attacks on Gaza-bound trucks in Israel, a group of Israeli activists on Sunday travelled with an aid convoy to protect it, an AFP correspondent said.
Aid has also begun entering via a temporary US-built floating pier, where shipments sent from Cyprus are offloaded for distribution.
The UN's humanitarian chief Martin Griffiths warned that if dire fuel shortages were not alleviated, the "famine which we have talked about for so long, and which is looming, will not be looming anymore. It will be present".
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