The warning came as Israel stepped up the renewed assault it launched on Tuesday, shattering the relative calm in the war-battered territory since a January 19 ceasefire.

A Palestinian source close to the ceasefire talks told AFP late Friday that Hamas had received a proposal from mediators Egypt and Qatar for re-establishing a truce and exchanging hostages for Palestinian prisoners "according to a timeline to be agreed upon".

The source said the proposal "includes the entry of humanitarian aid" into Gaza, which has been blocked by Israel since March 2.

Israel resumed intensive bombing of Gaza on Tuesday, citing deadlock in indirect negotiations on next steps in the truce after its first stage expired earlier this month.

The territory's civil defence agency said Israeli strikes killed 11 people on Friday -- three in pre-dawn strikes and eight more during the daytime.

On Thursday, it had reported a death toll of 504 since the bombardment resumed, one of the highest since the war began more than 17 months ago with Hamas's attack on Israel.

In a statement Friday, Katz said: "I ordered (the army) to seize more territory in Gaza... The more Hamas refuses to free the hostages, the more territory it will lose, which will be annexed by Israel".

Should Hamas not comply, Katz also threatened "to expand buffer zones around Gaza to protect Israeli civilian population areas and soldiers by implementing a permanent Israeli occupation of the area".

The military urged residents of the Al-Salatin, Al-Karama and Al-Awda areas of southern Gaza to evacuate their homes Friday ahead of a threatened strike.

AFP images from northern Gaza showed donkey carts piled high with belongings as residents fled their homes along rubble-strewn roads.

- 'Pressure points' -

Israeli forces said Friday that they had killed the head of Hamas's military intelligence in southern Gaza in a strike a day earlier, the latest official targeted in recent days.

Israel's resumption of large-scale military operations, coordinated with US President Donald Trump's administration, drew widespread condemnation.

Turkey's foreign ministry condemned what it called a "deliberate" attack by Israel on a Turkish-built hospital in Gaza.

"The IDF (military) struck terrorists in a Hamas terrorist infrastructure site that previously had served as a hospital in the central Gaza Strip," a military spokesperson told AFP in response to a question about the Turkish accusations.

In a statement, the health ministry in Hamas-run Gaza condemned "the heinous crime committed by the occupation (Israel) in bombing the Turkish-Palestinian Friendship Hospital", calling it "the only hospital designated for the treatment of cancer patients in the Gaza Strip".

The ministry said Israeli forces had used the hospital as "a base for its forces throughout the period of its occupation of the so-called Netzarim axis".

Israeli President Isaac Herzog expressed worry about the government's actions in a video statement Thursday, saying it was "unthinkable to resume fighting while still pursuing the sacred mission of bringing our hostages home".

Thousands of protesters have rallied in Jerusalem in recent days, accusing Prime Minister Benjamin Netanyahu of resuming military operations without regard for the safety of the hostages.

Of the 251 hostages seized during Hamas's October 7, 2023 attack, 58 are still held by Gaza militants, including 34 the Israeli military says are dead.

The Israeli military said Thursday that it had closed off the territory's main north-south route as it expanded ground operations that resumed on Wednesday.

- Projectiles from Gaza, Yemen -

Israel's military said late Friday that it had intercepted a missile launched from Yemen, after air raid sirens sounded in Jerusalem and parts of central Israel.

It is the fourth missile launched from Yemen towards Israel since Tuesday, after Huthi rebels threatened to escalate attacks in support of Palestinians following Israel's renewed attacks on Gaza.

Earlier in the day, the military said it intercepted two projectiles fired from northern Gaza, which Hamas's armed wing said was in response to "massacres against civilians".

Katz said that "We will intensify the fight with aerial, naval and ground shelling as well as by expanding the ground operation until hostages are freed and Hamas is defeated, using all military and civilian pressure points".

He said these included implementing Trump's proposal for the United States to redevelop Gaza as a Mediterranean resort after the relocation of its Palestinian inhabitants to other Arab countries.