But the prime minister said the nation remains “appalled” by the deaths of three British aid workers in an Israeli Defense Forces (IDF) strike this week.
He repeated calls for a “humanitarian pause” to allow more aid into Gaza.
Separately, the UK announced a Royal Navy ship is to be deployed to the region to help deliver aid.
The Foreign Office has pledged £9.7m for aid, equipment and expertise to help an international effort to establish a maritime aid corridor between Cyprus and Gaza.
Meanwhile, Foreign Secretary Lord Cameron warned that the UK’s backing of Israel’s right to self defence was “not unconditional”.
He wrote in the Sunday Times that “we expect such a proud and successful democracy to abide by international humanitarian law, even when challenged in this way”.
His comments came almost a week after seven humanitarian aid workers were killed in an Israeli strike in Gaza, an incident he described as “tragic and avoidable”.
Sunday marks six months since Hamas gunmen attacked southern Israel on 7 October, killing about 1,200 people and seizing 253 hostages.
About 129 hostages remain unaccounted for, with at least 34 presumed dead.
Since then, 33,137 people have been killed in Gaza, with more than 75,815 injured, the Hamas-run health ministry says.
“Six months later, Israeli wounds are still unhealed,” said Mr Sunak. “Families still mourn and hostages are still held by Hamas.
“And after six months of war in Gaza, the toll on civilians continues to grow – hunger, desperation, loss of life on an awful scale.”
He said the UK had been “straining every sinew” to get aid into Gaza and that it “must be flooded in”. He also repeated calls for an immediate humanitarian pause, leading to a “long-term sustainable ceasefire”.
“We continue to stand by Israel’s right to defeat the threat from Hamas terrorists and defend their security,” said Mr Sunak.
“But the whole of the UK is shocked by the bloodshed, and appalled by the killing of brave British heroes who were bringing food to those in need.”
Israel faced harsh criticism from its allies last week, after an IDF unit attacked a convoy of World Central Kitchen (WCK) vehicles from the air.
Seven people were killed in the attack, including three British military veterans who were acting as the convoy’s security team: John Chapman, 57, James “Jim” Henderson, 33, and James Kirby, 47.
Israel said the attack was a “grave accident” and has sacked two military officers after carrying out an inquiry.
Mr Sunak’s comments come after former prime minister Boris Johnson said it would be “shameful” for the UK to end arms sales to Israel.
Mr Johnson was responding to calls from some MPs to stop selling weapons to Israel after the IDF attack on the WCK aid workers.
More than 600 lawyers, including former Supreme Court justices, this week wrote to the government saying weapon exports to Israel must end because the UK risks breaking international law over a “plausible risk of genocide” in Gaza. Israel rejects the claim of genocide as “wholly unfounded”.
Labour’s shadow foreign secretary David Lammy also called for Israeli hostages to be returned home and condemned the “intolerable death and destruction” of the IDF’s military campaign.
Mr Lammy called for “an immediate ceasefire”.
Announcing the £9.7m aid package for Gaza, Lord Cameron warned in a statement of a real prospect of famine.
The foreign secretary said the UK, along with the US, Cyprus and other partners, will set up a temporary pier off the coast of Gaza.
The international plan, which aims to be up and running by early May, will see tens of thousands of tonnes of aid transported from Cyprus to Gaza via the pier.
The Foreign Office said the UK was continuing to call for urgent changes to the system, known as the deconfliction mechanism, for protecting humanitarian aid workers.