Brexit minister David Davis has said the UK and Republic of Ireland want to retain an open border.
Keeping the single energy market covering Northern Ireland and the Republic, exports and skills would also be important in making the departure a success for Northern Ireland, Mr Davis said.
Mr Davis met Stormont First Minister Arlene Foster and Sinn Fein Finance Minister Mairtin O Muilleoir during a visit to Belfast. He also met a group of business leaders at Stormont which has been established to advise the Northern Ireland Office on local concerns about Brexit negotiations.
Mr Davis said: “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.
Britain has been warned by the Irish government that any attempt to fortify the border with the Republic to prevent migrants slipping into the UK by the back door “won’t work”.
Irish foreign affairs minister Charlie Flanagan has insisted the two countries must keep the “invisible” border that exists at present after Brexit.
Northern Ireland Secretary James Brokenshire said there was strong will from both governments to ensure that there was no return to the borders of the past.
“We will work to achieve that, to ensure that that benefit is retained but we have the strength of that CTA that I think has suited both the UK and the Republic of Ireland very, very well for decades and how we want to see that continue.”
Mr Davis has said he wants to reach out to people in places which voted to remain in the EU and said there were big opportunities for exporters.
“We take looking after the regions and nations of Britain and the UK very seriously indeed.”
The DUP and Mr Davis campaigned for an exit.
DUP Stormont First Minister Arlene Foster said Northern Ireland should have a direct role in Brexit negotiations.
She did not share Mr O Muilleoir’s concerns that Northern Ireland would lose out on EU funding.
The First Minister said: “I am satisfied that we have clarity in relation to the spending of European funding up to 2020 and that is of course the only time up until which we can get clarity because that is the period of time up until which European funding has been paid up.”