An Israeli army self-propelled artillery Howitzer fires a shell toward the Gaza Strip on Friday. AFP

Israel ratcheted up its attacks in the south of the Gaza Strip on Saturday after Prime Minister Benjamin Netanyahu and US President Joe Biden discussed differences over a post-war future for Palestinians that have suggested a rift between the two allies.

Witnesses said the Israeli bombardment was again focused overnight on Khan Yunis, the largest city in Hamas-controlled Gaza's south, although Palestinian media also reported intense fire around Jabalia in the north early on Saturday.

Biden and Netanyahu held their first call since December 23 a day after the Israeli leader reiterated his rejection of any form of Palestinian sovereignty, deepening divisions with Israel's key backer over the war.

While the two leaders spoke of what might come next, the reality of the war was all too clear in Khan Yunis and elsewhere in the Hamas-controlled territory.

A Palestinian sits among destruction from the Israeli bombardment in the Nusseirat refugee camp in Gaza Strip. AP

A child with a bloodied face cried on a gurney at Al-Nasser hospital in Khan Yunis, while ambulances carrying the wounded and the dead arrived to the sound of automatic weapons in the distance.

Israel has vowed to destroy Hamas in response and its air and ground offensive has killed at least 24,762 Palestinians, around 70 per cent of them women, young children and adolescents, according to Gaza's Hamas-run health ministry.

Netanyahu has said Israel expects the war to continue for months, but his comments on Thursday rejecting a so-called two-state solution suggested a rift with key backer the United States.

Biden said after Friday's call with Netanyahu, with whom he has had a complicated relationship over some 40 years, it was possible the Israeli leader might still come around.

"There are a number of types of two-state solutions. There's a number of countries that are members of the UN that... don't have their own militaries," Biden told reporters after an event at the White House.

Mourners react during the funeral of a Palestinian man killed during an Israeli army military operation in Tulkarem. AFP

"And so, I think there's ways in which this could work."

Netanyahu said on Thursday Israel "must have security control over the entire territory west of the Jordan River", which "contradicts the idea of (Palestinian) sovereignty".

US Secretary of State Antony Blinken had said in Davos a day earlier that Israel could not achieve "genuine security" without a "pathway to a Palestinian state".

Agence France-Presse