The chancellor, Philip Hammond, has hit back at criticism of Theresa May’s Brexit deal, arguing that it is a better option than staying in the EU.

Hammond, who backed remain during the referendum, defended the prime minister’s exit strategy after the Democratic Unionist party leader, Arlene Foster, described it as a worse outcome for Britain than a Jeremy Corbyn government.

Hammond’s comments came as May travelled to Brussels where she was to hold talks with the European commission president, Jean-Claude Juncker, and the European Council president, Donald Tusk, before a summit of EU leaders on Sunday.

Asked on BBC Radio 4’s Today programme what he thought of Foster’s assessment of the deal, Hammond said: “Well, I don’t agree with it, obviously. There’s a [DUP] party congress going on, party leaders talk to their faithful.”

The chancellor met Foster on Friday night for talks over the government’s exit strategy, including the plan for a backstop allowing the Irish border to remain open.

Quick guide Brexit and backstops: an explainer Show Hide A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

Hammond added: “I hope that the conversations I had last night with Arlene Foster and many of her colleagues and the ongoing discussions that are happening between the two parties will lead to a solution.”

Asked whether he thought the deal was better than staying in the EU, he said: “I believe so, yes.”

When it was pointed out that he campaigned strongly for remain during the referendum, he said: “I campaigned originally in the referendum to remain in the European Union, but the outcome of the referendum was that a majority of people in this country voted to leave. The country is split down the middle, and what we have got to do now is bring the country back together so that we can move on and take advantage of the opportunities that are available to Britain in the future.”

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His defence comes after the former Brexit minister Dominic Raab, who quit the cabinet last week in protest at May’s Brexit strategy, said that the deal would be worse than the country staying the EU.

But Hammond said: “My response would be that remaining in the EU after we’ve had a clear referendum decision to leave the EU would be utterly debilitating to our politics. It would completely undermine confidence in the political system and it would leave very large numbers of people feeling let down, betrayed by the system.”

Asked whether May’s Brexit deal was a greater threat than a government led by Corbyn, Foster had told the Times: “I think it is, and the reason I say that is, on day one of us leaving the European Union there would be no difference, we would be exactly the same as the rest of the UK, but in year five or 10, we would be different.”

Hammond said Foster had not said the same to him when they met on Friday, adding: “I think that the Democratic Unionists have understandable concerns about anything which proposes solutions, even if they’re very unlikely to ever have to be brought into effect, where there would be any kind of difference in treatment between Northern Ireland and the rest of the UK. And I absolutely understand those concerns, and it’s our job to reassure them: firstly, that we’re never likely to get into that situation.

“Secondly, that we have done everything we possibly can to minimise any difference that there would be during any temporary backstop period, and that it only could only ever be a temporary period.”

Earlier in the programme, the former Northern Ireland secretary Theresa Villiers rejected May’s Brexit deal and said it should be renegotiated. If that could not be done, she said, “it would be with a very heavy heart that I would advocate the prime minister walks away from the negotiations and we step up preparations for leaving without an agreement”.

She admitted that could “lead to some disruption in the short term”, but added: “I think fairly soon we would see a resumption in negotiations.”