During the debate, protesters gathered outside Parliament to demand the end of arms sales to Israel, something that was repeatedly echoed by MPs, including former Labour leader Jeremy Corbyn.
The MP, who now sits as an independent, is calling for a public inquiry to uncover what he called the "murky history of what's gone on, the murky arms sales and the complicity in appalling acts of genocide".
He has tabled a draft bill to set up an inquiry to examine the "any UK military, economic or political cooperation" with Israel, with powers to question ministers and officials.
The bill is backed by prominent left-wing Labour MPs including Diane Abbott and Richard Burgon, four independent MPs, two Greens and members of Plaid Cymru and the SNP.
It has been scheduled for debate on 4 July, but is unlikely to become law without government backing.
Corbyn was among the MPs calling for a total embargo on the sale of arms to Israel - including parts for F-35 fighter jets.
Hamish Falconer said the UK had already taken steps to "ensure that weapons directly for use in Gaza have been suspended," and had stopped supplying F-35 parts "directly to Israel".
But he said the UK would continue to supply parts to the "global pool" of F-35 spares, as this was needed to help "the defence of Nato allies" and support the Ukraine war effort.
When it was put to him that Ukraine did not use F-35s, he said the planes were needed for the redeployment of F-15s, which were used in the fight against Russia.
But Corbyn and other critics insist the government's explanations lack credibility and they must know that the parts are being used to attack Palestinians in Gaza.
The Lib Dems are also urging a tougher stance from the government on Israel.
At prime minster's questions, Sir Ed Davey urged Keir Starmer to "push at the UN Security Council for humanitarian corridors to get the desperately needed aid urgently into Gaza".
Sir Keir said that the government is "working at pace with our allies on that very issue, to take whatever measures we can to get that humanitarian aid in".
Israel launched its military campaign in Gaza in response to Hamas' cross-border attack on 7 October 2023, in which about 1,200 people were killed and 251 others were taken hostage.
At least 54,607 people have been killed in Gaza since then, including 4,335 since Israel resumed its offensive on 18 March, according to the territory's health ministry.