Brexit minister David Davis has acknowledged that the Republic of Ireland and the UK 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 Northern Ireland's First Minister Arlene Foster and Sinn Féin Finance Minister Máirtín Ó 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 allows free movement of people between Ireland and the UK.
Britain has been warned by the 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".
Minister for Foreign Affairs 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."
Speaking afterwards Mr Ó Muilleoir said he "asked David Davis to underwrite Peace and Interreg applications post-autumn statement and to do so now and asked him to guarantee that EU citizens making their lives here would not be expelled under any circumstances.
"The economic, cultural and social damage an EU border - whether hard or soft - would have on the island of Ireland would be huge. And it would be most keenly felt in border areas."