Baroness Warsi has said in an interview that a Government minister has talked to her about resigning in protest over policy toward Israel and Hamas.
In an interview with Channel 4 News, the former Home Office minister added that there was "unease" on the backbenches over the Gaza conflict and said that one "senior Conservative" backencher had been "on the phone in tears".
She said she hoped her resignation would leave "people who feel the same as I do feel prepared to raise those voices within Government".
Baroness Warsi was hailed by David Cameron before the Conservatives came to power, but has now halted her rise through the party's ranks - quitting as Foreign Minister over the Government's policy on Gaza.
ITV News Political Correspondent Emily Morgan reports:
Deputy Prime Minister Nick Clegg says he wants to see arms licences to Israel suspended after the country "overstepped the mark" in its attacks on Gaza.
The Liberal Democrats leader said he shared Baroness Warsi's "concerns" over Britain's relations with Israel and said such licences should be halted pending an existing review of whether they should be revoked more permanently in future.
Baroness Warsi has given a statement to explain why she has resigned from the Foreign Office over the Government's policy on Gaza.
She was asked why she felt she would not have more influence remaining in Government rather than leaving her post.
Baroness Warsi has made a short statement following her resignation from the Foreign Office, claiming that she resigned because the Government's "morally indefensible" policy on Gaza "wasn't moving".
Over the last four weeks I have done everything I can both at formal meetings and informal meetings trying to convince my colleagues that our current policy on Gaza is morally indefensible, that it's not in British interests and that it will have consequences for us, both internationally and here at home.
In the end I felt the Government's position wasn't moving and I had to, on a point of principle, resign.
The Foreign Secretary has dismissed complaints from Conservative colleagues that the Government has failed to take a hard line against Israel over the Gaza conflict.
Philip Hammond said it was more important to engage in the peace process than to get involved in "megaphone diplomacy".
A letter from the Prime Minister to Baroness Warsi following her resignation said the government's policy on Gaza was "consistently clear" on the Gaza conflict and expressed disappointment that the two were "not able to speak about your decision beforehand".
I realise that this must not have been an easy decision for you to make and very much regret that we were not able to speak about your decision beforehand.
I understand your strength of feeling on the current crisis in the Middle East – the situation in Gaza is intolerable. 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.
David Cameron also praised the Baroness for her work in Government, adding that he was "sorry" to receive her signature.
Perhaps most importantly, I would like you to know how much I have personally appreciated your support and friendship over the years, and your commitment to our Party and the Government. You were one of the early supporters of my leadership campaign in 2005, something for which I remain grateful.
You can take pride in your achievements in Government and, especially, for being the first Muslim woman in any British Cabinet. I appreciate your assurance of support in the months and years to come and I hope that you will always feel able to raise any issue with me at any time.
Foreign Secretary Philip Hammond says Baroness Warsi's resignation from his department over Gaza "came as a surprise".
He said the former Foreign Office minister had done a "fantastic job" but added: "I do find it surprising that she has chosen now, this particular moment, to take this stand when at long last we are seeing some relief, some progress on the issues about which she was so passionately concerned."
Asked about the criticism of other politicians, who have called for tougher language against Israel, Mr Hammond said he had to take a more "dispassionate" view on the conflict to ensure peace.
Ed Miliband says Baroness Warsi has "acted with principle and integrity" in resigning from the Foreign Office over the Gaza conflict.
He added on Twitter that David Cameron should "break his silence" over Israel's "indefensible actions".
I think Baroness Warsi has acted with principle & integrity. People around Britain have been shocked by the suffering we have seen in Gaza.
David Cameron is right to condemn Hamas as a terrorist organisation but he needs to break his silence on Israel's indefensible actions.
Labour’s Shadow Foreign Secretary has said most reasonably minded people would "agree with the sentiments" expressed by Baroness Warsi in her resignation.
Most reasonably minded people across Britain will agree with the sentiments expressed by Baroness Warsi in her resignation statement today. It is a sad reflection of the Prime Minister’s misjudgement of the crisis in Gaza that this capable Minister has felt the need to leave the Government Labour has consistently opposed the Israeli incursion into Gaza and has repeatedly urged the Prime Minister to speak up and to speak out against the horrific loss of life witnessed in recent weeks, but he has so far failed to do so.