The newly-appointed Environment Secretary said the EU referendum result must be honoured but it is "really important" that the exit package is "in the interests of the whole country".
Pressed on reports of secret talks between Cabinet ministers and Labour MPs, Mr Gove said the two parties had a "similar" position on Brexit and the reality of the hung parliament meant the Government would have to "work with everyone".
He told Sky News: "I think the right thing to do is honour the vote that the British public made just a year ago.
"We voted then to take back control of our borders and our laws and to take back control of our money and trade deals.
"But it's also really important we make sure the Brexit deal we secure is one that's in the interests of the whole country and that means that we need to ensure that those who voted Remain are part of the conversation about what the best deal for Britain is in the future."
Mr Gove said: "Labour argued that we should leave the European Union and end free movement, in effect be outside the single market.
"Their position on this was very similar to the Conservative position according to their manifesto."
Asked if that meant the Government would work with Labour, Mr Gove replied: "Well the parliamentary arithmetic is such that we are going to have to work with everyone."
Mr Gove said the Tory failure to win a majority meant Brexit must proceed with the "maximum possible consensus".
Speaking on Radio 4's Today programme he said: "We as Conservatives were not returned with a majority and that means that we need to proceed with the maximum possible consensus and that we also need to make sure that the concerns of people who voted Remain, many of whom now actually want us to press ahead with leaving the EU as quickly and as in as orderly fashion as possible, but we need to make sure that their concerns are part of our conversation."
Asked about the possible formation of a cross party Brexit commission, he said: "I don't think that I should specify and I don't want to specify means by which we should involve everyone in our conversation but the House of Commons already has, as I say, a Brexit committee on which I served alongside Labour and Scottish Nationalist MPs and we produced reports, those reports were achieved by consensus.
"The most important thing is if you want to proceed with the maximum possible support that you engage in an open conversation and in that open conversation what you don't do is try to corral others into a particular position, you're true to your principles, true to the referendum result but open in the way in which you wish to engage."