The minister for exiting the European Union has said the UK is seeking tariff-free access to the EU.
David Davis said a good trading relationship is in the interests of the other members as well as Britain, but he warned the country has to take control of its borders and control the number of people coming in.
"What we will seek to do is ideally to have a tariff-free access, but this is a matter of negotiation, and we will be negotiating over an issue which I suspect we will find is in the interest of the other members of the EU as well as us, to get a good trading relationship in the long run."
Mr Davis was in Belfast for talks with Stormont First Minister Arlene Foster and Sinn Fein.
Northern Ireland voted to remain in the EU in the June 23 referendum.
Prime Minister Theresa May has pledged to get "the best deal" for British business in negotiations over the UK's withdrawal from the European Union.
Cabinet ministers meeting at Chequers on Wednesday agreed that any Brexit deal will have to include controls on EU migration, sparking speculation that this will dash any hopes of full access to the single market for British companies.
Mr Davis said: "I agree with the Prime Minister, as you might expect, 100% on the priorities she put yesterday, but the simple fact is this: we have to, as a result of the biggest mandate in the UK's history, we have to take control of our borders, we have to be able to control the number of people coming into the UK."
Mr Davis met business leaders in Northern Ireland as well as members of Stormont's power-sharing ministerial Executive.
Mrs May has promised no return to the hard borders of the past after concerns that immigration controls could be reintroduced at Northern Ireland's land border with the Republic.
Mr Davis said the UK and Ireland wanted to maintain an open frontier.
"We have had a common travel area throughout the UK and the Republic of Ireland for many, many decades before we were part of the EU and we will maintain that common travel area afterwards.
"We managed to do that without an immigration problem in that time."
The Common Travel Area (CTA) allows free movement of people between Ireland and the UK.
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