Instead, the paper proposes a "new customs partnership" or "highly streamlined customs arrangement" aimed at avoiding a hard border on the movement of goods. There should be "no physical infrastructure at the border", it said.
The proposals include a cross-border trade exemption for smaller traders and an agreement on regulatory equivalence for agri-food, as a means of minimising sanitary and phytosanitary checks.
The government will protect the common travel area and associated rights for UK and Irish citizens, and put upholding the Good Friday agreement "at the heart of its exit negotiations", the paper said.
The proposed customs agreement must ensure that as long as Ireland remains a member of the EU, Irish citizenship also confers EU citizenship, with all the rights that go with this, the paper said. "This is as true for the people of Northern Ireland who are Irish citizens – or who hold both British and Irish citizenship – as it is for Irish citizens in Ireland."
The Irish government said it welcomed the publication of the paper.
"The emphasis on the priority areas identified by the government, including the common travel area, the Good Friday agreement, north/south cooperation and avoiding a hard border, is welcome. Protecting the peace process is crucial and it must not become a bargaining chip in the negotiations," it said.
Guy Lougher of Pinsent Masons, the law firm behind Out-Law.com said: "The paper indicates clearly that the government is very alive to the particular circumstances of Northern Ireland’s interactions with Ireland, and is looking to preserve the status quo as far as possible."
"The suggestion of a cross-border trade exemption for smaller traders would address many of the UK's concerns about the potential adverse impact of enhanced customs processes on cross-border trade, and especially in the agri-food sector, but the EU is likely to be concerned that it could create precedents elsewhere. That suggestion and the suggestion of regulatory equivalence for agri-foods are potentially significant given the proportion of cross-border trade accounted for by agri-food businesses," Lougher said.
"The paper raises a number of issues on which the EU will require the UK government to provide further detail on its proposals, but there will also be a need for the EU to consider how it will respond to the broad principle suggestions which the UK government has made," he said.
The position paper follows the release of a paper yesterday which proposed similar arrangements for the UK's borders with the EU as a whole. That paper also said that the UK hopes to continue its current customs arrangements with the EU for a period of time after Brexit.
A "model of close association with the EU customs union for a time-limited interim period" would benefit both the UK and EU member states, it said.
The EU's chief negotiation on Brexit, Michel Barnier, said on Twitter yesterday that "the quicker #UK & EU27 agree on citizens, settling accounts and #Ireland, the quicker we can discuss customs & future relationship."
Northern Ireland Secretary James Brokenshire told the BBC that he believed that the EU would be open to the government's proposals.
"If you look at what Michel Barnier has said and others within the EU, 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.
"I think there is a shared objective that we have, that the EU has and the Irish government has, in finding that solution."