Efforts to persuade MPs to back Theresa May’s Brexit deal will continue on Thursday, a day after she promised to quit as PM if it was approved.

Her pledge brought some on-side, such as ex-Foreign Secretary Boris Johnson.

But challenges remain for the PM after Northern Ireland’s DUP, who she relies on for support, said it would not back the deal because of the Irish backstop.

Meanwhile, none of eight alternative Brexit proposals brought by MPs secured backing in a series of Commons votes.

The options – which included a customs union with the EU and a referendum on any Brexit deal – were supposed to help find a consensus over how best to leave the EU.

But the failure of any of them to garner support from a majority of MPs led Brexit Secretary Stephen Barclay to say it strengthened ministers’ view their deal was “the best option”.

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Ahead of the debate heralding the “indicative votes”, Mrs May told a meeting of Conservative backbenchers she would leave office earlier than planned if it guaranteed Parliament’s backing for her withdrawal agreement with the EU.

Mrs May told her MPs: “I have heard very clearly the mood of the parliamentary party. I know there is a desire for a new approach – and new leadership – in the second phase of the Brexit negotiations – and I won’t stand in the way of that.”

She told MPs she would resign as party leader after 22 May – the new Brexit date – but stay on as PM until a new leader is elected. However, Downing Street said it would be a “different ball game” if the deal was not passed.

Her announcement that she would not lead the talks with Brussels over the future relationship between the UK an EU prompted a number of Tory opponents of her deal to signal their backing.

Prominent Leave supporters such as Mr Johnson and former Tory leader Iain Duncan Smith said they now viewed the deal as the least-worst option.

Media captionArlene Foster: ‘Backstop makes it impossible for us to sign deal’

But Mrs May needs to win over 75 rebels to overturn the 149-vote rejection of her deal on 13 March.

Jacob Rees-Mogg, who chairs the Brexiteer European Research Group (ERG), said he would only support the deal if the 10 MPs of the DUP did so.

“I won’t abandon the DUP because I think they are the champions of the Union of the United Kingdom,” he told the BBC.

The DUP’s main objection is to the backstop, the “insurance policy” designed to avoid the return of border checkpoints between Northern Ireland and the Republic of Ireland in the event a future trade deal is not agreed.

It argues that the measure would result in Northern Ireland having to abide by different trade rules to the rest of the UK, which leader Arlene Foster says would “damage the Union”.

“The backstop in that Withdrawal Agreement makes it impossible for us to sign up to the agreement,” she told the BBC.

Meanwhile, ERG vice-chairman Steve Baker suggested he may resign the Conservative whip rather than vote for the deal.