Stephen Barclay said he has told chief Brexit negotiator Michel Barnier that he wants a deal but will leave the EU on October 31 with or without one.
The Brexit minister said that he spoke to Mr Barnier on Tuesday and relayed the government's intention over exiting the bloc.
He wrote in a tweet: "Spoke to Michel Barnier today and made our position clear: We want a deal but are leaving the EU on October 31 with or without one."
Mr Barclay, the Tory MP for North East Cambridgeshire, voted Leave in the 2016 referendum.
A prominent Brexiteer, he became the third Brexit Secretary in six months under Theresa May after Dominic Raab resigned from the post.
He retained the position in Boris Johnson's dramatic Cabinet reshuffle.
Before that, he had been a minister of state in the health and social care department, the rank below cabinet level.
