Brexit Secretary Dominic Raab said a deal with Brussels will have to be agreed by the end of November.
And he insisted the UK has compromised as much as we can on the crucial Irish border issue.
But European leaders set up a massive showdown as one of Emmanuel Macron's closest allies said "the ball is in London's court".
Theresa May this week failed to strike a Brexit deal during an EU summit in Brussels.
And EU leaders refused to set a date for a possible emergency summit next month, raising the prospect a deal could be pushed back to December.
Mr Raab told the BBC's Andrew Marr Show that delaying a deal until the end of the year wouldn't work, because there wouldn't be enough time to push it through Parliament.
He said: "I'm confident we can get a deal, and equally I think we need to have done it by towards the end of November."
The minister added that Mrs May should refuse EU demands for a "backstop" which would either carve off Northern Ireland from Britain, or keep the whole UK in Europe's customs union permanently.
Mr Raab said: "We've made concessions, we've made compromises – there does come a point where you can be compromised yourselves by the compromises you make.
"That's why we need to have to be very clear that Northern Ireland cannot be separated from the rest of the UK in customs or regulatory terms, and we cannot have a situation where we're stuck in an indefinite limbo.
"They're the Government's red lines, and the Cabinet's."
France's Europe minister Nathalie Loiseau issued a challenge to the PM – telling Marr: "We need to fix the answer of the Irish border.
"We need to have a British answer to what we have proposed, the ball is in London's court.
"We can't have temporary measures that disappear and we don't know what to do after that."
But in a boost for Mrs May, she confirmed that Mr Macron would back a special November summit to sign off on a Brexit deal.
The EU wants Britain to agree to a backstop which would prevent a hard border in Ireland if the two sides fail to address the issue in a future free-trade agreement.
Mr Raab said the backstop would only work if there were a way for the UK to pull out of it in future.
He said: "It could be time limited, there could be another mechanism – there needs to be something which allows us to control how long we’re there for."
The Brexit Secretary also confirmed that Britain is considering signing up to extend the transition period which is due to end in December 2020.
That would effectively delay the moment when the UK actually leaves the EU.
Mr Raab's predecessor David Davis today laid out his own "Brexit manifesto" in what will be seen as an attempt to position himself as a possible replacement for Mrs May.
He blasted the PM, saying she'd "managed to anger not just Leavers but ardent Remainers as well".
And he called on ministers to bar European planes from British airspace if Brussels continues to play hardball with the UK.
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