Palestinian president Mahmoud Abbas's Fatah movement called on its Islamist rivals Hamas on Saturday to relinquish power in order to safeguard the "existence" of Palestinians in the Gaza Strip.

"Hamas must show compassion for Gaza, its children, women and men," said Fatah spokesman Monther al-Hayek.

He called on Hamas to "step aside from governing and fully recognise that the battle ahead will lead to the end of Palestinians' existence" if it remains in power in Gaza.

Hamas seized power in Gaza in 2007 from the Fatah-dominated Palestinian Authority, and subsequent attempts at reconciliation have failed.

The territory has been devastated by an Israeli offensive in retaliation for the assault by Hamas and other Palestinian militants on Israel on October 7, 2023.

Following disagreements over the next steps in a January 19 ceasefire in the Gaza war, Israel resumed air strikes on Tuesday, followed by ground operations the day after.

On Friday, Israeli Defence Minister Israel Katz threatened to annexe parts of Gaza unless Hamas frees the remaining Israeli hostages seized in the October 7 attack.

Of the 251 hostages taken that day, 58 are still being held, including 34 the Israeli military says are dead.

Hamas's 2023 attack on Israel resulted in 1,218 deaths, mostly civilians, according to Israeli figures.

Nearly 50,000 people in Gaza have been killed in the war, according to the Hamas-run territory's health ministry. (AFP)