The government has said there must be an "unprecedented solution" for the border between Northern Ireland and the Republic after Brexit.
A paper detailing its proposals focuses on the need to avoid a hard border.
The government stresses there should be no physical infrastructure, such as customs posts, at the border, which has almost 300 crossing points.
Critics say the proposals lack credible detail, with Labour deriding the plans for the border as "a fantasy frontier".
The government's paper does not envisage CCTV cameras or number plate recognition technology at the border, or set back from it.
Instead, the government is arguing for a wide-ranging exemption under which small and medium-sized businesses will not have to comply with any new customs tariffs.
Northern Ireland is the only part of the UK that will share a land border with an EU state post-Brexit.
The future management of that border is a highly sensitive issue and is one of three main priorities in UK-EU Brexit negotiations.
Northern Ireland Office officials say 80% of firms in Northern Ireland are small or medium sized and engaged in local business rather than international trade.
If the proposals are accepted, customs officials envisage using a mix of technology and physical checks to monitor the compliance of bigger businesses engaged in international trade.
Such firms might be required to declare their import and export businesses online.
The government has repeated its desire to maintain the Common Travel Area and the rights of UK and Irish citizens, and to uphold the 1998 Good Friday Agreement, of which the UK is a co-guarantor.
Prime Minister Theresa May said she wanted to reassure nationalists living in Northern Ireland.
"No one voted to end the special ties between the UK and Ireland, or to undermine the unique arrangements between Ireland and Northern Ireland which have underpinned the peace process and have been in place well before our membership of the EU," she said.
Irish Foreign Minister Simon Coveney said he broadly agreed with the position paper's "aspirational" principles.
"They reflect a lot of the language that the Irish government has been using, actually, in terms of maintaining the status quo, frictionless borders," he said.
Designed to reassure the European Union
Adam Fleming, BBC Brussels Reporter
The European Commission responded to the publication of the UK paper by saying there had to be a political deal to protect the Good Friday Agreement before a discussion could begin on technical measures.
The paper is full of language and examples designed to soothe the EU about its worries.
Michel Barnier said the Good Friday Agreement must be guaranteed. The UK said it would be.
The Common Travel Area, which allows free movement between the UK and Ireland, is enshrined in an EU Treaty and letting it continue wouldn't be illegal under European Law.
One British official said privately that if no agreement is reached, EU rules would compel the Irish government to introduce the hard border it does not want.
Labour's spokesman on Northern Ireland, Stephen Pound, said an ID card system would have to be introduced to manage immigration after Brexit.
"The idea of having a CGI, virtual reality border is nonsense, it's just a pipe dream but the second thing is it's about goods, it's not about people," he said.
Labour leader Jeremy Corbyn said he had discussed the issue at length with EU chief negotiator Michel Barnier during a meeting in Brussels, in which he said there must be no hard border.
"I hope there can now be negotiations to make sure there is a continuation of absolute free movement between the Republic and Northern Ireland," he said.
Critics argue the re-introduction of the hard border would severely damage the Northern Ireland peace process and have a negative economic impact.
A European Commission spokeswoman said: "We must discuss how to maintain the Common Travel Area and protect, in all of its dimensions, the Good Friday Agreement.
"It is essential that we have a political discussion on this before looking at technical solutions."
Sea border dismissed
The position paper forms part of the government's negotiations with the European Union, ahead of the UK leaving the EU in March 2019.
As revealed on Tuesday, Brexit Secretary David Davis wants a limited transition period to implement any new customs arrangements, including considerations relating to the "unique circumstances" of Northern Ireland and the Republic of Ireland.
Both the UK and Irish governments have repeatedly stated their opposition to a hard border, but the situation is complicated as the UK intends to leave the EU's customs union.
The position paper sets out two "broad approaches" to future customs arrangements that the UK hopes will help to prevent physical customs posts along the Irish border.
The suggestions are a "new customs partnership" or a "highly streamlined customs arrangement".
The partnership model would "align" customs approaches between the UK and the EU, resulting in "no customs border at all between the UK and Ireland," the paper claims.
The paper suggests the second, "highly-streamlined" arrangement could include:
- A continued waiver on submitting entry/exit declarations
- Continued membership of the Common Transit Convention to help Northern Ireland and Irish companies transit goods
- A new "trusted trader" arrangement for larger businesses
- A "cross-border trade exemption" which would mean no new customs processes at all for smaller traders
The paper also dismisses the idea of a customs border in the Irish Sea, saying it would be economically and constitutionally unviable.
It recognises that all this needs to be negotiated with the EU, in the hope that the border between the EU and the UK will be as "seamless" as possible.
Northern Ireland Secretary James Brokenshire said he did not accept that the EU would be unwilling to facilitate the government's proposals.
"If you look at what [EU chief negotiator] Michel Barnier has said... there is a recognition that there will need to be specific arrangements in relation to customs and other elements in terms of creating that frictionless border," he said.
"There is a shared objective that we have, that the EU has and the Irish government has, in finding that solution."
UK-Irish trade in numbers
- £13.6bn worth of goods exported to the Republic of Ireland from Great Britain in 2016
- £9.1bn worth of goods exported to Great Britain from the Republic of Ireland in 2016
- £10.7bn worth of goods from Northern Ireland were sold in Great Britain in 2015
- £2.7bn worth of goods from Northern Ireland were exported to the Republic of Ireland in 2015
- More than 80% of cross-border trade on the island of Ireland is by small and medium-sized enterprises (SMEs)
The Ulster Unionist Party welcomed the government's position paper, while Democratic Unionist Party leader Arlene Foster said it was a "constructive step".
"It is clear the government has listened to voices in Belfast, Dublin, Brussels and London about how the United Kingdom's only EU land border could be managed after we exit the EU," said Mrs Foster, NI's former first minister.
However, Sinn Féin northern leader Michelle O'Neill said Northern Ireland was "a fleeting concern for the British government, we are collateral damage".
"What we need to see is the Irish government acting in the national interest and defending the rights of those people here in the north that voted to stay with the European Union," she said.
Colum Eastwood, leader of the Social Democratic and Labour Party (SDLP), said the government seemed to be "effectively playing for more time".
What is the customs union?
Countries in the customs union do not impose tariffs - taxes on imports - on each other's goods.
Every country inside the union levies the same tariffs on imports from abroad.
So, for example, a 10% tariff is imposed on some cars imported from outside the customs union, while 7.5% is imposed on roasted coffee.
Other goods - such as soap or slate - have no tariffs.
The UK has said it is leaving the EU's customs union because as a member it is unable to strike trade deals with other countries.