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16 November 2018, 10:13 | Updated: 16 November 2018, 10:24
He warned Conservative backbench "Leavers" they run the risk of the UK staying in the EU if they oppose Theresa May's plan.
Mr Cairns also stated his support for the Prime Minister after leading Brexiteer Jacob Rees-Mogg submitted a letter of no confidence in her leadership.
The Welsh Secretary spoke on Thursday evening after hosting a Board of Trade meeting at Swansea University alongside International Trade Secretary Liam Fox.
Dr Fox refused to speak to the press at the university after he had earlier batted off suggestions he should resign over the draft EU withdrawal agreement.
Asked about the wave of ministerial resignations and calls for Mrs May to be ousted as Prime Minister, Mr Cairns said the Government's lack of a majority in Parliament meant any successor would find it equally hard to satisfy all parties.
Mr Cairns said: "Changing the prime minister doesn't change the arithmetic of Parliament, so therefore colleagues need to accept the context in which we're working in.
"I would say to the hardliner Leavers who want to leave without a deal that they run the risk of not having a Brexit.
"And I would say to the ones who are Remainers who want to ignore the outcome of the referendum that they're running the risk of leaving without a deal, which is the worst that each side would want.
"So this tries to bring together a pragmatic solution that takes control of our laws, our borders and our money, and on that basis we'll be honouring the outcome of the referendum.
"We'd be an independent trading nation once again, and I suspect if David Cameron had offered this at the time he came back from European negotiations I suspect there would've been a massive majority for it."
Mr Cairns admitted the draft agreement was a "compromise", and described the "backstop" plan to prevent a hard border in Ireland as a "negative" aspect.
Mr Cairns had earlier hosted the first ever Board of Trade meeting in Wales with Dr Fox, who announced an Energy Investment Portfolio worth an estimated £240 million for the country.
He said: "This is the first time the Board of Trade have ever met in Wales and I think that demonstrates we're already now planning for that time beyond Brexit.
"This is about taking those opportunities, about being that independent trading nation where we can strike trade deals right around the globe, and where we continue to access the European market."