The Liberal Democrats are calling for the suspension of arms export licences to Israel, adding to the pressure David Cameron is facing over Gaza.
It comes after Baroness Warsi resigned as a Foreign Office minister, arguing Downing Street's stance on Israel's actions was "morally indefensible".
She said the government was not doing enough to shape events, but the PM said he had been clear in calling for peace.
No 10 said a review of arms export licences was already under way.
Israel launched Operation Protective Edge last month with the stated aim of ending rocket attacks and destroying tunnels used by Palestinian militants.
Gaza officials say the conflict has killed 1,800 Palestinians, while 67 Israelis have also died. The two sides agreed a 72-hour ceasefire, which came into force at 08:00 local time (05:00 GMT) on Tuesday.
Deputy Prime Minister Nick Clegg said the Israeli military operation in Gaza had "overstepped the mark" and called for the suspension of arms export licences to Israel.
He said he had been working with his Lib Dem colleague and business secretary Vince Cable to get the suspension finalised, saying an announcement would be made "very shortly".
Speaking about the potential suspension of licences, Mr Cable said senior Lib Dems had been "making this case inside government", but said they had "not yet been able to get agreement" with Tory coalition partners.
"I hope and expect that to change shortly," he said.
Conservative MP and former Chief Whip Andrew Mitchell also said an embargo "should be considered", telling BBC Radio 4's World at One there was "a strong case for trying to ensure that weapons getting into this conflict are minimised as much as possible".
A Downing Street spokesman said a review of export licences to Israel was under way, and no new military licences had been issued since the Israeli operation was launched.
"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," the spokesman said.
The prime minister has faced criticism from several politicians - including Labour leader Ed Miliband - for not being more outspoken about Israel's actions.
After resigning on Tuesday, Lady Warsi said there was "unease" among Conservative backbenchers and "concern" at ministerial level over the government's position on Gaza, adding: "I've had a minister in a late-night conversation talking about resignation."
In her letter to the prime minister, Lady Warsi - the first Muslim woman to serve in a British cabinet - said: "I must be able to live with myself for the decisions I took or the decisions I supported. By staying in government at this time I do not feel that I can be sure of that."
Her decision followed criticism from several Conservative MPs that Israel's response to rocket attacks by Hamas militants in the West Bank and Gaza had been "disproportionate", a sentiment echoed on Tuesday by London Mayor Boris Johnson.
In his response to Lady Warsi's resignation, Mr Cameron wrote that he understood her "strength of feeling on the current crisis", saying the situation in Gaza was "intolerable".
'No need to go'
"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," he said.
Sir Hugh Robertson, who was a Foreign Office minister alongside Lady Warsi until he left in last month's reshuffle by Mr Cameron, said he was "sad" she had stepped down and understood why she felt "very strongly" about the situation in Gaza.
But he said he was "not sure that British policy towards the Middle East has changed markedly in the last fortnight", and he suggested "shouting" from London was not the best way to influence Israeli policy.
This view was contradicted by Lib Dem Energy Secretary Ed Davey, who said he shared Lady Warsi's views, but added: "I think she didn't need to go because we are winning the argument."
The Commons International Development Committee has said Mr Cameron should do more to persuade Israel to lift restrictions on the movements of Palestinians.
Several newspapers have reported that Mr Cameron is facing a growing "revolt" among senior Conservative MPs over Gaza.
The Times newspaper quoted Conservative MP Dominic Grieve, the former attorney general who was replaced last month, as questioning whether Israel's actions had been "reasonable, necessary and proportionate".