Stephen Barclay has said Brexit talks are nearing the “moment of truth” following a meeting in Brussels with EU chief negotiator Michel Barnier.
The UK was “committed to securing a deal” but there had to be “political will on both sides” and the backstop “has to go”, the Brexit secretary said.
Mr Barnier told Mr Barclay a deal must include a solution to prevent a hard Irish border, it was reported.
BBC Brussels correspondent Adam Fleming described the mood as “downbeat”.
He said European diplomats thought the chances of finalising a new Brexit deal by a crucial EU summit on 17 October were “dwindling”.
The UK is scheduled to leave the EU on 31 October, although MPs have passed a law requiring Prime Minister Boris Johnson to seek an extension to that deadline from the bloc if he is unable to pass a deal in Parliament, or get MPs to approve a no-deal Brexit, by 19 October.
“I think there is still a long way to go. I think we are coming to the moment of truth in these negotiations,” Mr Barclay said after Friday’s talks.
“We are committed to securing a deal. The prime minister has made clear he wants a deal, but there has to be political will on both sides and that’s what we are exploring.”
He said he had made “clear” that for a deal to happen “the backstop has to go”.
The policy is unacceptable to many Conservative MPs, and Mr Johnson has insisted a revised Brexit deal must include the abolition of the backstop.
The European Commission said Mr Barnier had stressed to Mr Barclay during the meeting that it was “essential” there was a “fully operational solution in the withdrawal agreement to avoid a hard border on the island of Ireland, protect the all-island economy and the integrity of the single market”.
“The EU remains open and willing to examine any workable and legally operative proposals that meet all these objectives,” a statement issued after the meeting said.