Business Secretary Greg Clark has told ITV's Peston he wants to see unity in Parliament as Labour make a pitch for a possible customs-union solution to the Brexit impasse.
Mr Clark told host Robert Peston the close referendum result means MPs across the chamber need to come together to find a compromise in the Brexit negotiations.
He also told Peston he would do everything he can to avoid a no-deal Brexit, hinting he may even resign if he can no longer influence events.
Mr Clark spoke after Labour leader Jeremy Corbyn and his aides made the case for a comprehensive customs union with the European Union in a meeting with Prime Minister Theresa May.
Mr Corbyn, who had initially refused to engage in cross-party talks with the prime minister until no-deal was taken off the table, described his meeting with Mrs May as "exploratory on the issues".
Asked by Peston about the likelihood of him backing a long-term customs union solution if it commanded a majority in the Commons, Mr Clark said: "I would want to see what proposals were there... you’re talking about a proposal that hasn’t even been made, let alone proposed for agreement.
"But as I said at the beginning I’ve always thought that when you have a 52-48 result in the referendum you have to have a deal that respects the fact that it was close, tries to bring the country together and when you followed that with a general election that didn’t have a majority, I think it’s incumbent on Parliament."
When pressed by Peston on whether he would resign over the possibility of a no-deal Brexit becoming a reality, he said: "I see signs of progress in Parliament coming together and my view is that while you have an ability to influence those discussions I don’t think it’s right to desert your post."
His party colleague Oliver Letwin told the programme he believed the UK would end up with a no-deal Brexit as Prime Minister Theresa May wouldn’t be able to come back from Brussels with anything that passes through Parliament.
Asked about the risk of a no-deal Brexit, the Tory MP said: "Enormously high, I think. I think the great likelihood is that is where we will end up, as things currently stand."
Labour MP Lisa Nandy meanwhile told Peston her party also need to start compromising and dropping some of their Brexit red lines in order to avoid a no deal.
She said: "It’s also incumbent on the Labour Party now to start making real choices about what it is that we want because we're two and a half years on from the referendum and there’s still a debate going on within the Labour Party about whether we respect the result of the referendum or whether we have a second referendum.
"We went into the 2017 election saying that we respected the result of the referendum."
She added: "My view is that that is important, but that means that we have to start compromising and we have to start dropping some of the red lines that are stopping us to getting to a deal or we will by default end up with no deal.
"And what you saw yesterday was a lot of MPs trying to hide behind process because they don’t want to make a decision about what happens next, in every political party, and that cannot be allowed to go on.”
Shadow cabinet minister Jon Trickett also said he welcomed the news that the government wants to protect workers’ rights after Brexit.