Theresa May still hopes to bring her Brexit deal back to parliament for a third meaningful vote this week, after the leading Eurosceptic Jacob Rees-Mogg said he was reluctantly considering supporting it.

The prime minister’s spokesman said there had been a long discussion at cabinet on Tuesday morning about how to respond to MPs’ vote to seize control of the parliamentary timetable.

But he said the government’s focus remained on trying to find a majority for May’s deal.

“If we are able to hold and win a vote this week, we will be able to leave the EU in two months, which is what the PM firmly believes is the right thing,” the spokesman said.

Asked whether May was hopeful she could yet win over her party, he said “the prime minister and her colleagues understand the need to work hard on this in order to build support”, adding that ministers would continue to hold meetings with MPs from different parties.

The hopes of some in government were buoyed by Rees-Mogg on Tuesday, as he indicated he could back the prime minister’s Brexit deal rather than risk Britain’s departure from the EU being delayed or abandoned.

But the Democratic Unionist party (DUP), her unofficial coalition partners, repeated that its MPs would not vote for the agreement as it stood.

It also remains to be seen how many other Tory MPs in the pro-Brexit European Research Group could follow the lead of Rees-Mogg, who chairs it, with a number of them still insisting they could not support May.

It emerged on Tuesday that May is going to address Conservative MPs at a meeting of the 1922 Committee on Wednesday night – with speculation swirling at Westminster that she could take the opportunity to name a date for her departure, in the hope of winning over more MPs to support her deal.

Speaking to the Conservative Home website for his regular “Moggcast” podcast, Rees-Mogg said fellow ERG members had to recognise they did not have the House of Commons votes to deliver their version of Brexit, and should see departure as a gradual process.

“We have to recognise that what we want and what we can deliver is not necessarily the same because of our lack of numbers,” he said. “The ERG and other Eurosceptics in parliament cannot win any vote on our own.”

Rees-Mogg said May had effectively ruled out a no-deal departure. “The prime minister will not deliver a no-deal Brexit,” he said. This meant, he argued, the options now appeared to be narrowing to being between her deal and potentially not leaving at all.

“That, I think, [could] become the choice, eventually,” he said. “Whether we’re there yet is another matter. But I’ve always thought that no deal is better than Mrs May’s deal, but Mrs May’s deal is better than not leaving at all. And so there is a sort of hierarchy of choice.

“And if the choice is the one that you suggest then, inevitably, leaving the European Union, even leaving it inadequately and having work to do afterwards, is better than not leaving at all. And perhaps the thought processes that people like me hadn’t gone through before is the thought that Brexit is a process rather than an event.”

Many Brexiters had viewed the process as being “29 March, we leave, that’s it, bingo, done”, Rees-Mogg added, and had to adjust their expectations. “If we take this deal, we are legally out of the European Union,” he added.

However, a series of other ERG members remain resolutely opposed to backing May’s plan, with one, Andrea Jenkyns, tweeting that it was “fake news” to suggest she might change her mind.

May also needs to secure the DUP’s 10 votes, a prospect that remains unlikely. On Tuesday, the DUP MP Jim Shannon insisted the party could not back the plan. “The obvious thing for us is that nothing has changed,” he told BBC Radio 4’s Today programme.

The only way for the DUP to support the plan, he said, was for the government to attach a time limit to the backstop insurance policy for the Irish border, which the EU has repeatedly ruled out.

“We had only one red line, and that red line was clear – the backstop. And that hasn’t changed,” Shannon said.

A change of heart by the ERG would not affect this, he added: “They maybe see Brexit as the greater issue, rather than the union. We see the union as the big issue, the priority.”