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.
Speaking in the Commons on Tuesday, Brexit minister James Duddridge said the government would "set out more detail on an alternative to the backstop in the coming days".
He also said he wanted to "assure the House there will be no infrastructure checks or controls at the border".
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 where ministers have made a raft of policy announcements, including raising the National Living Wage.
But the plans have been overshadowed by allegations that Mr Johnson squeezed the thigh of journalist Charlotte Edwards under a table at a lunch in 1999.
Asked about the accusation, the PM told BBC Breakfast it was "not true", but it was "inevitable" he would face "shot and shell" because of his stance on Brexit.
According to leaked proposals, the government has accepted there must be customs checks on the island of Ireland, but they would be conducted away from the border - mostly where goods originate or at their final destination.
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.
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."
Irish Taoiseach Leo Varadkar said the UK government had promised Ireland and the EU there would be no hard border as a result of Brexit, and they expected that commitment to be honoured.
"No British government should seek to impose customs posts between Northern Ireland and the Republic of Ireland against the will both of the people in Northern Ireland and the people here in the Republic of Ireland," he said.
Mr Varadkar went on to say that in the event of a no-deal Brexit, there would be checks at ports and airports.
'Very good offer'
Government sources accused unnamed individuals in the European Commission of leaking the suggestion in an effort to create "a hostile reaction" to their revised Brexit deal.
A European Commission spokesperson said they would not be commenting on the reports, but their position remained that they had "not received any proposals from the UK that meet all the objectives of the backstop".
Mr Johnson told the BBC he would not reveal details of the proposals to be put to the EU at this stage, but the UK would be making "a very good offer".
Crux of the problem here is what it has always been - Johnson’s position makes extra checks the logic - the massive challenge is how and where and if anything can be acceptable to the EU side— Laura Kuenssberg (@bbclaurak) October 1, 2019
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.
Labour's Hilary Benn asked an urgent question in the Commons about the government's plans for the island of Ireland.
"Today there are no border posts or checks on goods crossing the border... and the backstop is there to ensure that remains the case after Brexit.
"The government's position now, however, is that the reality of Brexit will require customs check on the island of Ireland - that is the inexorable logic of the prime minister's statement this morning."
He added: "It is unacceptable for us to be kept in the dark about what is being proposed in our name on such an important matter."
The Northern Irish DUP MP, Gregory Campbell, supported the government and said the House should "draw a little comfort" from the fact the EU appeared to have shifted somewhat from its previous position of refusing point blank to re-open the withdrawal agreement.
"At least that is a glimmer of light," he said.
But the SNP's Peter Grant said the "future of peace and normality on the island of Ireland will critically depend on the action of this prime minister" and claimed governments around the EU were beginning to believe Mr Johnson "could not be trusted".
Earlier, 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: "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."