Brexit Secretary David Davis has said that finding a solution to the issue of the border between Northern Ireland and the Republic would be "difficult", but can be done.
He also talked up the importance of maintaining the common travel area.
"What that means is we don't check up on Irish people coming in or vice versa," Mr Davis said.
"We treat Irish citizens just like British citizens and they treat British citizens just like Irish citizens.
"That's a very important part of our relationship. I think these are difficult problems, but they're all soluble.
Earlier, the minister downplayed the prospect of customs checks for lorries entering Britain following Brexit, claiming it was possible to have a "pretty frictionless arrangement".
He was unable to give guarantees there would be no checks, but said it was in both sides' interests to minimise disruption.
Elsewhere, at an event in Dublin, Catherine Day, special advisor to European Commission President Jean-Claude Juncker, said the common travel area could be maintained post-Brexit.