David Cameron is facing fresh pressure over Gaza in the wake of Baroness Warsi's resignation, with his Liberal Democrat coalition partners demanding the suspension of arms export licences to Israel.
Deputy Prime Minister Nick Clegg said he agreed with former Foreign Office minister Lady Warsi that there were "serious questions" about the licences.
"It's obvious to me that however much Israel has every right to defend itself from those rocket attacks from Hamas, nonetheless the Israeli military operation overstepped the mark in Gaza," Mr Clegg said.
"This outrageous spectacle of these three UN schools being hit by Israeli military action. That's why I believe that the export licences should now be suspended.
"I'm working with (Business Secretary) Vince Cable on this.
"It is his department that administers these export licences and he and I both believe the actions of the Israeli military, overstepping the mark in Gaza, breach the conditions of those export licences and that's why we want to see them suspended pending a wider review of whether they should be revoked more permanently in the long run."
The Government has already launched a review of export licences, but no decisions have been taken on suspension.
Mr Cable said: "Both Nick Clegg and I agree that we should suspend export licences for military equipment that might be used by Israel in Gaza. We have been making this case inside Government but have not yet been able to get agreement for this position. I hope and expect that to change shortly."
In an interview with Channel 4 News about her resignation, Lady Warsi branded the UK's policy on Gaza "mealy-mouthed" and "morally indefensible".
She said she discussed resignation in private with at least one other minister, and described having a telephone conversation with a Tory backbencher who was in tears at the devastation being shown on television.
The peer suggested she might have been able to stay in government if she had been a minister at another department such as transport, but could not continue defending the policy as the Foreign Office spokeswoman in the House of Lords.
"For me it's morally indefensible where after four weeks of a conflict, more than a quarter of the Gazan population displaced, nearly 2,000 people killed, 400 innocent children killed - we still cannot find the words to say we condemn this and that we feel that this action has been disproportionate," Lady Warsi said.
"These issues are far too serious for us to be mealy-mouthed and for us to be dragging our heels.
"I think there is a sincerely held view in government that the best way to resolve this matter is to try and be as accommodating as possible to the Israeli government, to try and through that seek influence with them, and through that to try and move them to a more positive decision. I'm not sure that policy is working."
Lady Warsi took particular aim at Chancellor George Osborne, who earlier complained that her departure had been "unnecessary", accusing him of failing to challenge Tel Aviv about its actions.
"George is a very good friend of the Israeli government and therefore he more than anybody else should have been saying quite frankly to the Israeli government that what you are doing is not in your interests - this is probably the biggest single act of self-harm that the Israeli government have done over the last few years," she said.
"What he should have been saying to the Israeli government is that it is unnecessary for you to kill innocent civilians, it is unnecessary for you to displace a quarter of the population, it is unnecessary for you to flatten schools, hospitals and power supplies and water supplies to achieve your ends.
"And had George done that, then I agree with him, it would not have been necessary for me to resign."
A Downing Street spokesman said: "A cross-Government review of export licences to Israel is under way following the sustained barrage of rocket attacks from Gaza into Israel which prompted Israel to launch Operation Protective Edge. Since then no new licences have been issued for use by the Israeli military.
"Suspending export licences is not a decision we take lightly and it is right that we examine the facts fully. This is the approach being taken by the vast majority of countries.
"We welcome the current ceasefire and the withdrawal of Israeli troops from Gaza, and continue to call for a political solution to be found."