The Israeli military said on Saturday it had seen a "significant movement" south of Palestinian civilians, a day after ordering Gaza City residents to flee, as Israel's prime minister promised further retaliation for Hamas' rampage last week.

US President Joe Biden said consultations were under way with regional governments on the humanitarian crisis in Gaza as trapped Palestinians endured a power blackout and shortages of food and water amid fierce Israeli bombing.

Israel has vowed to annihilate Hamas for the attack a week ago, in which its fighters killed 1,300 Israelis, mainly civilians, and seized scores of hostages.

Israel has since put the Hamas-run Gaza Strip, home to 2.3 million Palestinians, under a total siege and bombarded it with unprecedented air strikes. Gaza authorities say 1,900 people have died.

On Friday, more than one million residents of northern Gaza received a notice from Israel to flee south within 24 hours, a deadline that passed at 5am local time.

"We have seen a significant movement of Palestinian civilians towards the south," Israeli military spokesperson Lieutenant Colonel Jonathan Conricus told a video briefing early on Saturday. He did not mention the deadline and did not take questions.

Hamas vowed to fight to the last drop of blood and told residents to stay.

Tens of thousands of Palestinians were estimated to have headed south from northern Gaza after the Israeli order, according to the United Nations, which said more than 400,000 Palestinians had been internally displaced due to hostilities before the directive.

Many others, however, said they would stay. "Death is better than leaving," said Mohammad, 20, outside a building smashed by an Israeli air strike near the centre of Gaza. Mosques broadcast the message, "Hold on to your homes. Hold on to your land."

Biden said addressing the humanitarian crisis was a top priority. "The overwhelming majority of Palestinians had nothing to do with Hamas and Hamas' appalling attacks," Biden said. "And they're suffering as a result as well." (Reuters)