Theresa May will continue to sell her Brexit withdrawal deal on Friday, as cabinet minister Michael Gove is understood to be considering quitting.
BBC political editor Laura Kuenssberg said she understood Mr Gove had rejected the PM’s offer to make him Brexit secretary, because Mrs May would not let him renegotiate the deal.
Dominic Raab quit the role on Thursday over “fatal flaws” in the agreement.
Mrs May says the deal “delivers what people voted for”.
But she was warned by one of her own backbenchers that it was “dead on arrival” and would never get the backing of MPs.
The government unveiled its long-awaited draft withdrawal agreement on Wednesday, which sets out the terms of the UK’s departure from the EU, over 585 pages.
The prime minister will answer callers’ questions about the plan on LBC radio on Friday morning.
Asked about Mr Gove on Thursday, Mrs May said he was doing “an excellent job” as environment secretary, adding: “I haven’t appointed a new Dexeu [Department for Exiting the European Union] secretary yet and I will be making appointments to the government in due course.”
But the BBC understands Mr Gove, a leading Leave figure during the EU referendum, rejected her offer to make him Brexit secretary, saying he would only accept it if he could try to make changes to the negotiated deal – something Mrs May and EU leaders have made clear is not possible.
Mr Gove is said to have been key to getting backing for Mrs May’s deal at a lengthy cabinet meeting on Wednesday – during which a number of ministers expressed doubts.
Former Brexit Secretary Dominic Raab and Work and Pensions Secretary Esther McVey both went on to quit over the agreement.
The draft agreement has also upset some Tory backbenchers, including leading Brexiteer Jacob Rees-Mogg, who said he and others had submitted letters of no confidence in Mrs May to the chairman of the Conservatives’ backbench 1922 Committee.
Forty eight letters are needed to trigger a confidence vote.
It is understood that a group of cabinet ministers are also considering whether to try to force Mrs May to make some changes to the withdrawal deal.
‘Right for our country’
The agreement sets out commitments over citizens’ rights after Brexit, the proposed 21-month transition period, the £39bn “divorce bill” and, most controversially, the “backstop” to avoid a hard border between Northern Ireland and the Republic of Ireland.
It still needs to get the stamp of approval from MPs in Parliament, and finally from the 27 other EU member states.
Mrs May issued a defiant message in Downing Street on Thursday, saying: “I believe with every fibre of my being that the course I have set out is the right one for our country and all our people.”
She added: “Leadership is about taking the right decisions, not the easy ones.”
She acknowledged some were not happy with the compromises made to secure the deal, but said it “delivers what people voted for and it is in the national interest”. She also vowed to “see this through”.
But Labour Leader Jeremy Corbyn told her: “The government simply cannot put to Parliament this half-baked deal that both the Brexit secretary and his predecessor have rejected.”
And Liberal Democrat leader Sir Vince Cable suggested the PM was “in denial”, adding she had “rightly conceded that ‘no Brexit’ is the real alternative”.
By BBC Political Editor Laura Kuenssberg
The government, for today at least, is at the mercy of events, not in control.
Theresa May’s vow to stay does not make her deep, deep problems disappear.
With her party in revolt, her colleagues departing – some determined to usher her out of office – we can’t, and don’t know yet, if Brexit can happen as planned, perhaps, if at all.
This could be a gale that’s weathered in a few days, or a serious storm that sweeps the government away.
Read Laura’s blog
Elsewhere, some of Mrs May’s own backbenchers warned the deal would not command support in the House of Commons, when it is put to a vote in early December.
Tory MP Mark Francois said that with Labour, the SNP, the Lib Dems and Northern Ireland’s DUP planning to vote against it – alongside, he said, more than 80 Tory MPs – it was “mathematically impossible to get this deal through the House of Commons” and it was “dead on arrival”.
However during a press conference in Downing Street, Mrs May said abandoning the withdrawal deal would be “to take a path of deep and grave uncertainty when the British people just want us to get on with it”.