Israel's armed forces bombarded Gaza on Sunday, but officials also said diplomatic efforts were expected to resume in coming days towards a truce and hostage release deal.
Air strikes and artillery shelling rained down again overnight on northern, central and southern area of Gaza in the more than seven-months-old war sparked by Hamas's October 7 attack.
Fighting has centred on the far-southern city of Rafah, where Israel has vowed to destroy the last remaining Hamas battalions despite a chorus of international opposition to a ground invasion of the city.
Israel's assault there from early May led Egypt to shut its side of the Rafah border crossing -- but on Sunday, aid trucks from Egypt again rolled into Gaza, this time via the nearby Kerem Shalom crossing.
US President Joe Biden said Saturday his administration was engaged in "urgent diplomacy to secure an immediate ceasefire that brings hostages home".
Mediator Egypt was also continuing "its efforts to reactivate ceasefire negotiations", said Al-Qahera News, which has links with Egyptian intelligence.
Israeli media has said intelligence chief David Barnea had agreed a new framework for talks on a ceasefire in a meeting with America's CIA chief and Qatari mediators in Paris.
An Israeli official, requesting anonymity, told AFP on Saturday that "there is an intention to renew these talks this week".
However, senior Hamas official Osama Hamdan told Qatar's Al Jazeera network that so far "there is nothing practical on this issue. It is just talk coming from the Israeli side."
- Bodies pulled from rubble -
Israeli Prime Minister Benjamin Netanyahu has come under increasing domestic pressure over the fate of the hostages, with demonstrators rallying again in Tel Aviv on Saturday.
In recent days, the bodies of seven dead hostages have been retrieved from Gaza, heightening the fear and pain of relatives of the remaining captives.
In Tel Aviv, a crowd of several thousands observed a minute of silence Saturday for dead captives.
"I feared this moment," Avivit Yablonka, whose brother Chanan was brought back dead from Gaza, told the rally. "I will continue to shout, support, fight and do everything so that all the hostages return home."
Hamas meanwhile said Saturday it had taken "prisoner" at least one Israeli soldier in an ambush in Jabalia camp.
The claim was denied by the army, which said there was "no incident in which a soldier was abducted".
The war broke out after Hamas's October 7 attack on southern Israel, which resulted in the deaths of more than 1,170 people, mostly civilians, according to an AFP tally based on Israeli official figures.
Militants also took 252 hostages, 121 of whom remain in Gaza, including 37 the army says are dead.
Israel's retaliatory offensive has killed at least 35,903 people in Gaza, mostly civilians, according to the Hamas-run territory's health ministry.
The UN has warned of looming famine in the besieged territory, where most hospitals are no longer functioning.
In the latest fighting, Gaza's civil defence agency said Sunday it had retrieved six bodies after a house was targeted in a strike on Rafah's eastern Khirbet al-Adas neighbourhood.
Witnesses said Israeli artillery had also targeted central Rafah's Yibna camp, and that heavy artillery shelling hit the city's Sooq al-Halal and Qishta neighbourhoods.
Elsewhere in Gaza, Israeli air strikes targeted the Nuseirat camp, and witnesses said heavy artillery shelling hit northern Gaza.
Israeli tanks in Gaza City rained heavy gunfire on targets in the Zeitun and Netzarim area, an AFP reporter said.
Israel's military meanwhile said Sunday the arrival of aid had been stepped up, both via a new US-built pier and through its own land crossings, Kerem Shalom and Erez West.
"This week, after the pier began operating for the first time, a total of 1,806 pallets of food were transferred in 127 trucks to logistics centres of international aid agencies in the Gaza Strip," it said.
"In total, this week, 2,065 humanitarian aid trucks were inspected and transferred through the Kerem Shalom and Erez West crossings, which is almost twice the number in the previous week."
US Central Command said Saturday that four US Army vessels supporting the pier broke free of their moorings, and had run aground in heavy seas, with Israel aiding the recovery effort.
- Global pushback -
As the bloodiest ever Gaza war grinds on, Israel has faced heavy global pushback over the surging civilian death toll and the destruction of vast swathes of Gaza.
In the past week it faced landmark moves from two international courts based in The Hague and from three European governments.
Last Monday, the prosecutor at the International Criminal Court said he would seek arrest warrants on war crimes charges against Netanyahu and his defence minister as well as against three top Hamas figures.
On Wednesday, Ireland, Norway and Spain said they would recognise Palestinian statehood by May 28, a move Israel angrily rejected as a "reward for terrorism".
And on Friday, the International Court of Justice ordered Israel to halt its Rafah offensive, demanded the release of hostages and urged the "unhindered provision" of humanitarian aid into Gaza.
The ICJ ruling came in a case brought by South Africa alleging that Israel's military operation amounts to "genocide".
It ruled that Israel must "immediately halt its military offensive, and any other action in the Rafah governorate, which may inflict on the Palestinian group in Gaza conditions of life that could bring about its physical destruction in whole or in part".
Israel has denied any military operations in the Rafah area that "could cause the destruction of the Palestinian civilian population, in whole or in part".