Baroness Warsi became the first minister to quit the Tory-Lib Coalition because of principle rather than scandal.
In an extraordinary parting shot, the former Foreign Office minister warned the current policy on Gaza also ran counter to Britain's national interest.
And she suggested it had been apparent in recent weeks how much the government missed experienced colleagues like Ken Clarke, sacked by Mr Cameron in a reshuffle last month.
In response, the Chancellor George Osborne described her resignation as "disappointing and frankly unnecessary".
Downing Street was more diplomatic, saying that the Prime Minister regretted her decision.
It later emerged that Mr Cameron had been informed she was standing down only moments before it was announced on social media.
In a letter to Lady Warsi he wrote: "I ... very much regret that we were not able to speak about your decision beforehand."
In an exit interview with the Huffington Post website Lady Warsi, a former Tory party chairman, also called for a UK ban on the sale of weapons to Israel.
Ministers are reviewing all export licences to Israel following international outrage at the numbers who have died in recent days.
Today Mr Cameron comes under more pressure over his policy on Gaza as MPs call on the Prime Minister to do more to persuade Israel to lift its block on the movements of Palestinians.
The Commons International Development Committee warned that some controls on Gazans, who are rarely allowed to leave the territory, were not compatible with international law.
Both the Prime Minister and the Chancellor insisted that the UK was doing everything it could to bring about a ceasefire.
Mr Cameron wrote: "I understand your strength of feeling on the current crisis in the Middle East. Our policy has always been consistently clear: we support a negotiated two-state solution as the only way to resolve this conflict once and for all and to allow Israelis and Palestinians to live safely in peace."
But others backed her decision. Labour's shadow foreign secretary Douglas Alexander said: "Most reasonably-minded people will agree with the sentiments she expressed."
In her resignation letter, Lady Warsi said: "My view has been that our policy in relation to the Middle East peace process generally, but more recently our approach and language during the current crisis in Gaza, is morally indefensible, is not in Britain's national interest and will have a long-term detrimental impact on our reputation internationally and domestically."