The UK will send two Royal Navy ships and surveillance aircraft to the eastern Mediterranean in plans to “bolster security”, No 10 says.
The aircraft will begin patrols on Friday to “track threats to regional stability such as the transfer of weapons to terrorist groups”.
Three Merlin helicopters and a detachment of Royal Marines are also being dispatched.
Rishi Sunak spoke to Israel’s PM on Thursday to reaffirm the UK’s support.
His call to Israeli Prime Minister Benjamin Netanyahu was meant to “reaffirm the UK’s steadfast support for Israel following Hamas’ appalling terrorist attack”, Downing Street said.
“The additional military assistance would be deployed in the coming days to bolster security in the wider region and mitigate any attempts to escalate the conflict,” it added.
“He [Mr Sunak] reiterated that the UK stands side by side with Israel in fighting terror and agreed that Hamas can never again be able to perpetrate atrocities against the Israeli people.
“Noting that Hamas has enmeshed itself in the civilian population in Gaza, the Prime Minister said it was important to take all possible measures to protect ordinary Palestinians and facilitate humanitarian aid.”
The two prime ministers “agreed to remain in close contact and to explore any further support the UK can provide”.
The prime minister said earlier: “Our military and diplomatic teams across the region will also support international partners to re-establish security and ensure humanitarian aid reaches the thousands of innocent victims of this barbaric attack from Hamas terrorists.”
He also asked for military teams in Israel, Cyprus and across the region to be bolstered to support contingency planning.
Mr Sunak spoke to Egyptian President Abdul Fattah al-Sisi on Thursday morning to discuss the importance of opening the Rafah crossing into Gaza to allow for humanitarian access and provide a route for British and other nationals to leave.
More on Israel Gaza war
Hamas launched an unprecedented attack on southern Israel on Saturday, killing at least 1,300 and taking around 150 hostages to Gaza.
More than 1,300 have also been killed in Gaza since Israel launched retaliatory air strikes.
Defence Secretary Grant Shapps said the military aid would be an “undeniable display of the UK’s resolve to ensure Hamas’s terrorist campaign fails”.
The Foreign Office has begun arranging flights for British nationals stranded in Israel. The first plane is expected to leave Tel Aviv on Thursday, with more planned “in the coming days, subject to security”.