Short breaks in hostilities could allow hostages and British nationals out of the besieged enclave, the prime minister said.
But a wholesale ceasefire would only benefit Hamas, two weeks after it killed 1,400 people in Israel and seized more than 200 hostages, No 10 said.
Mr Sunak’s call echoes that of the United States, the United Nations and other countries for specific pauses, as distinct from a ceasefire, to alleviate what many fear is becoming a full-scale humanitarian crisis as water, medical supplies and fuel run out.
Labour was also plunged into crisis over its stance on Israel’s bombardment of Gaza, with Keir Starmer under mounting pressure from Muslim MPs and others to call for a ceasefire.
It came as:
the UN warned aid workers could be forced to halt humanitarian operations if Israel does not lift its blockade on fuel due to run out tonight
UN chief Antonio Guterres denied a "blood libel" justification for Hamas’s terror after he said the deadly 7 October attack “did not happen in a vacuum"
Lebanese militant group Hezbollah met with Hamas and Islamic Jihad to discuss what their alliance must do to achieve “real victory for the resistance” in Gaza
The UK sent an RAF plane to Egypt with 21 tonnes of humanitarian supplies
As the crisis mounted, the UN agency for Palestinian refugees, the largest provider of humanitarian services in Gaza, said it would run out of fuel by Wednesday night. Officials said they were forced to reduce their operations as they rationed what little fuel they had.
Mr Sunak told MPs at Prime Minister’s Questions that the UK has already discussed the idea of pauses with other countries at the United Nations.
He said the government wanted Britons to be able to leave Gaza, for hostages to be released and for supplies to cross over into the area. “And we recognise for all of that to happen there has to be a safer environment, which of course necessitates specific pauses, as distinct from a ceasefire,” he said.
His call came hours after the US Secretary of State Antony Blinken defended Israel’s military actions but said that “humanitarian pauses must be considered” to protect civilians in Gaza.
Calls for “humanitarian pauses” could be included in a UN Security Council Resolution, No 10 indicated. Unlike a ceasefire, these would be temporary and limited in scope. How they would work and and how long they might last were for discussion, Downing Street said. Israeli agreement to a series of pauses in the conflict would be a question “for them”,
Mr Sunak made the call as he announced that an RAF plane was en route to Egypt with 21 tonnes of humanitarian supplies.
Mr Sunak also rejected calls for him to back a ceasefire, reiterating the government’s stance that Israel has the "right to protect itself" after suffering a "shockingly brutal terrorist attack" at the hands of Hamas.
No 10 said a wholesale ceasefire “would only serve to benefit Hamas”.
Labour backed the call for specific pauses in the conflict. Labour leader Sir Keir Starmer refused to give in to those urging him to call for a ceasefire in Gaza, but backed Mr Sunak’s support for “humanitarian pauses” in the conflict.
A spokesman for the Labour leader said: “Antony Blinken said ... humanitarian pauses must be considered. That seems to be something that Downing Street is now echoing and we would obviously fully support that position.”
UNRWA, the UN agency for Palestinian refugees, has warned it could halt operations in Gaza on Wednesday night because of the lack of fuel.
“If we do not get fuel urgently, we will be forced to halt our operations in the Gaza Strip. Time is running out,” UNRWA spokesperson Tamara Al-Rifai told the BBC.