Any agreement to allow an extended Brexit transition should be instead of - not as well as - a "backstop" to avoid the return to border checks in Ireland, the Brexit secretary has said.
The 21-month transition is currently expected to end on 31 December 2020 - but an extension was floated during last week's EU summit.
The idea angered Leave-supporting MPs.
But Dominic Raab says it should be instead of a backstop - the nature of which is also controversial.
It comes after hundreds of thousands of protesters marched through London on Saturday, calling for a referendum on the outcome of the Brexit negotiations.
Meanwhile, negotiators are at loggerheads over how best to avoid checks coming in on the Irish border after the UK leaves the EU.
The UK and EU are agreed on the need for a "transition period" - which Theresa May calls an implementation period - designed to smooth the path between the UK leaving the EU on 29 March next year, and a new permanent relationship with the bloc, including a new trading agreement, coming into force.
During that period, which ends on 31 December 2020, the UK's relationship would remain largely the same as at present.
But in case there is a gap between that period ending, and a long-term UK-EU relationship coming into force, the EU has proposed that Northern Ireland remain in the EU customs union for a period to avoid the need for customs checks on the border with the Irish Republic.
The UK government is opposed to this, because it would mean that Northern Ireland had a different set of rules to the rest of the UK - it argues it would effectively create a new border down the Irish Sea.
Prime Minister Theresa May's alternative backstop proposal is that the whole of the UK would temporarily stay in the customs union.
Mrs May suggested last week that the period could be extended by "a matter of months" if it helped to avoid a "hard border" with the Irish Republic.
However, this angered some pro-Brexit campaigners, who said it would leave Brussels with too much power in negotiations.
Writing in the Sunday Telegraph, Mr Raab said there should be no "indefinite limbo" inside the EU's customs union.
But he added: "The prime minister has rightly refused to rule out considering different approaches - including extending the implementation period for a limited period of a few months, as an alternative to the backstop.
"But we won't sacrifice Northern Ireland, and we must have finality to any backstop - whether through a time-limit or a mechanism that enables the UK to leave, in case the EU doesn't live up to its promise to get the future relationship in place swiftly."
It comes as a former Brexit minister is trying to put a legal barrier in the way of the EU's backstop plan by requiring the approval of the Stormont Assembly.
Northern Ireland's devolved government has not sat since power-sharing collapsed in January 2017.
And on Saturday, an estimated 700,000 people marched through central London to demand a referendum on the final Brexit deal.
Mayor of London Sadiq Khan - who started the march - was among those who addressed a rally in Parliament Square, along with representatives from the main political parties.
Celebrity speakers included Steve Coogan, Delia Smith and Deborah Meaden.
At the same time, former UKIP leader Nigel Farage led a pro-Brexit rally in Harrogate, North Yorkshire.
He said: "The evidence suggests about a third of those that voted remain now say we're democrats and think the government should simply get on with it.
"And that's our message - get on with it, fulfil your promises to us, you said if we voted to leave it would happen, it needs to."