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.
Sources also accused unnamed individuals in the European Commission of trying to create “a hostile reaction” to their revised Brexit deal in order to put pressure on the government to make more concessions.
But a European Commission spokesperson said they would not be commenting on the reports, adding they had “not received any proposals from the UK that meet all the objectives of the backstop, as we have been reiterating and demanding”.
The UK is set to leave the EU on 31 October.
Mr Johnson has said the exit will go ahead with or without a deal – despite MPs passing a law last month forcing him to ask for an extension from the EU if Parliament hasn’t voted in favour of a specific deal or leaving without one.
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 in 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 told Breakfast: “They are not talking about the proposals that we are actually going to be tabling.
“They are talking about some stuff that went in previously.”
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”.
We don’t have the exact proposals from the UK government, but we’re beginning to get the shape of it.
Yes, there will be customs checks, but no, there won’t be a hard border, and no, these checks won’t be done five or 10 miles away from the border.
The government is saying we can do most of them in the depots and warehouses before lorries even leave.
In some instances, there will be physical inspections, but then it will be up to customs authorities to decide where to do them – it might be at the depots or they might want their own physical area to carry them out.
The problem with that is the Irish government and the EU don’t want any checks at all, because they view them as a hardening of the border even if it isn’t a hard border.
The view of the British government is that life can’t just carry on the same as before because we are leaving and we want to have our own trade policy.
Tory MP and chairman of the pro-Brexit European Research Group Steve Baker said there would be “some additional checks” after Brexit, but that was “inescapable”.
He told BBC News: “People need to face up to the true reality here. We are leaving, and that, I am afraid, will mean some change to the status quo.
“But I’m absolutely confident this can be a world class border with a real minimisation of inconvenience to businesses and individuals – consistent with the kind of approach adopted today.”