The Government has been plunged into turmoil after Foreign Office Minister Baroness Warsi dramatically stormed out, saying David Cameron's policy on Gaza was "morally indefensible".

Lady Warsi, who was the first Muslim minister to sit in Cabinet, said she could not support a position which ran counter to Britain's national interest and risked radicalising a new generation of young Muslims.

Her resignation was met with ill-disguised fury among Mr Cameron's inner circle, with Chancellor George Osborne branding her action "disappointing and unnecessary".

But the move prompted renewed calls from some senior Conservatives for the Government to take a tougher line with Israel over its incursion into Gaza in the face of rising Palestinian casualties.

There were concerns among some Tories that - with the general election just nine months away - the Government's stance could cost them the support of Muslim voters in key battleground constituencies.

Athough Lady Warsi had been signalling her concern over the Government's position for some time, her decision to walk out appeared to have taken No 10 by surprise.

With Mr Cameron out of the country on holiday in Portugal, she did not even wait for the traditional exchange of letters with the Prime Minister, using her Twitter page to post her letter on the internet.

"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," she wrote.

In his reply, Mr Cameron expressed "regret" that they had been unable to speak before she made her decision to go.

"I understand your strength of feeling on the current crisis in the Middle East - the situation in Gaza is intolerable," he wrote.

"Of course, we believe that Israel has the right to defend itself. But we have consistently made clear our grave concerns about the heavy toll of civilian casualties and have called on Israel to exercise restraint, and to find ways to bring this fighting to an end."

Mr Osborne was scathing about her decision to leave, just as a humanitarian ceasefire between Israel and Hamas finally appeared to be holding.

"This a disappointing and frankly unnecessary decision," he said. "The British Government is working with others in the world to bring peace to Gaza and we do now have a tentative ceasefire which we all hope will hold."

Foreign Secretary Philip Hammond said: "I do find it rather surprising that she has chosen now, this particular moment, to take this step when, in fact, we are now at long last seeing some relief, seeing some progress on the issues about which she was so passionately concerned."

Ministers will be concerned that a series of senior Conservatives spoke out to express support for her action.

Former justice minister Crispin Blunt said she had been "brave and principled" while Sarah Wollaston praised her "principled stand", adding: "I hope it changes policy."

Senior backbencher Nicholas Soames said the Government needed to "note and learn", saying: "She was right to leave over a matter of such great importance."

London mayor Boris Johnson said he hoped she would return to the Government "as soon as possible", while he condemned the Israeli action as "disproportionate" - a word Mr Cameron and Mr Hammond have consistently avoided.

"I can't for the life of me see how this can be a sensible strategy," he said during a LBC radio phone-in. "I think it is disproportionate, I think it is ugly and it is tragic and I don't think it will do Israel any good in the long run."

Mr Hammond was dismissive, insisting the Government's position was geared towards achieving a long-term political solution to the crisis.

"To my colleagues who say can you do a bit more megaphone diplomacy over here or over there, offend one side or the other side a bit more, I say it is more important to achieve the result we all want to see," he said.

The drama unfolded just days after Downing Street reacted furiously to a call by Ed Miliband for the Government to take a firmer line on Israel, with No 10 accusing the Labour of trying to "play politics" with the issue.

Mr Miliband said today that Lady Warsi had acted with "principle and integrity" and urged Mr Cameron to re-think his position.

"I hope that David Cameron will reflect on what she says in her resignation letter and change his approach," he told BBC News.

"He needs to break his silence and say that Israel's actions have been unjustified and indefensible. He needs to show that he can be even-handed and, without fear or favour, argue for the long-term solution that we need to this tragic conflict."

In her resignation letter, posted on her Twitter page, Lady Warsi hinted that she was unhappy at the impact of changes in last month's Cabinet reshuffle - including the replacement of William Hague as foreign secretary by Mr Hammond.

"There is, however, great unease across the Foreign Office, amongst both ministers and senior officials, in the way recent decisions have been made," she wrote.

She also highlighted the departures of Cabinet veteran Ken Clarke and Dominic Grieve, the former attorney general, both seen as strong upholders of international law.

She pointed to evidence emerging from the Home Office suggesting the fallout from the conflict in Gaza and Britain's response to it would be a basis for radicalisation which "could have consequences for us for years to come".

Lady Warsi became the first Muslim to sit in the Cabinet when she was made Conservative Party co-chairman by David Cameron following the 2010 general election.

She was subsequently moved to the post of minister of state at the Foreign Office and minister for faith and communities in Mr Cameron's 2012 reshuffle in a move widely regarded as a demotion.