Boris Johnson says the “reality” of Brexit is there will need to be customs checks on the island of Ireland after the UK leaves the EU.
But the PM rejected claims that would effectively mean a hard border, in the form of a series of customs posts set five or 10 miles back.
He told BBC Radio 4’s Today programme: “A sovereign united country must have a single customs territory.”
He refused to give details, but said formal proposals would be made soon.
Government sources told the BBC on Monday night it had prepared the legal text of an updated Brexit deal and would be making more plans public in the coming days.
The issue of the Irish border – and how to keep it free from border checks when it becomes the frontier between the UK and the EU – has been a key sticking point in Brexit negotiations.
The current government says the solution reached by the EU and Theresa May, the backstop, is unacceptable and an alternative to it must be found.
Mr Johnson was speaking at the start of the third day of the Conservative Party conference in Manchester.
The government has made a raft of policy announcements, including raising the National Living Wage over the next five years and investing into roads and bus networks.
But the plans have been overshadowed by allegations that Mr Johnson squeezed the thigh of a journalist under a table at a lunch in 1999.
Asked about the allegation by Charlotte Edwardes in the Sunday Times, the PM told BBC Breakfast: “They’re not true. It’s obviously very sad that someone should make such allegations.”
Mr Johnson also said it was “inevitable” he would face “shot and shell” because of his stance on Brexit.
But after No 10 first denied the accusation on Sunday evening, Ms Edwardes tweeted: “If the prime minister doesn’t recollect the incident then clearly I have a better memory than he does.”
The BBC’s Iain Watson said according to leaked proposals, the government accepts there must be customs checks on the island of Ireland, but they would be conducted away from the border.
Customs formalities would be carried out mostly where goods originate or at their final destination.
The Irish broadcaster RTE had reported that a “string of customs posts perhaps five to 10 miles away from the frontier” had been floated by the UK.
But Ireland’s Deputy Prime Minister Simon Coveney said the plans were a “non-starter”, tweeting that Northern Ireland and the Republic of Ireland “deserve better”.
The prime minister insisted “that’s not what we’re proposing at all”.
He would not reveal details of the proposals to be put to the EU, telling Today he “would like to veil our proposals in decent obscurity” before sharing them.
But Mr Johnson said this was the “moment the rubber hits the road” and the UK would making “a very good offer”.
He also insisted the government had made “a great deal of progress” in negotiations since August, and they were working “flat out to get a deal”.
Just as with Theresa May, customs is proving to be the sticking point for this prime minister.
He, however, is taking a different attitude towards what a potential solution might be.
Boris Johnson explicitly denied the suggestion that came out overnight that there will be a string of customs points on either side of the Irish border.
However, we heard him clearly accept that the concept of having more checks will be part of the proposal he puts to Brussels in the next couple of days.
So, an explicit denial on the specifics of this idea, but an acceptance this concept is something real, is something that the UK government is going to pursue and that, of course, is extremely difficult for the other side.