Northern Ireland Secretary of State James Brokenshire says he believes a positive outcome can be reached in keeping the Irish border open after Britain leaves the EU.
The fate of the 310-mile frontier has been plunged into uncertainty, amid fears for the peace process and the island's cross-border economy, since the Brexit referendum result in June.
The issue was top of the agenda as Mr Brokenshire made his first official visit to Dublin for only his second face-to-face meeting with Irish Foreign Affairs Minister Charlie Flanagan since his appointment in July.
Speaking ahead of their talks, the Secretary of State refused to be drawn on whether the UK will also pull out of the EU customs union - which many observers say will force the return of a hard border in Ireland.
But he suggested a solution could be created around the common travel area, a decades-old agreement between both countries which allows Irish and British citizens to cross internal borders without controls.
"No decisions have been taken in relation to the customs union," he said.
"I would stress that really strong will, that strong commitment, on the UK Government's part, working with the Government of Ireland, to see that we do create that solution around the common travel area."
Mr Brokenshire added: "I stress the priority I give as Secretary of State around this, knowing that there is that strong will, that strong intent and how we will seek to achieve that positive outcome, which I think is attainable."
Mr Flanagan has already signalled Ireland is cautious of British reassurances there will be no return to a hard or heavily militarised border on the island.
The border between Northern Ireland and the Republic of Ireland will also become an EU frontier after Britain leaves the European bloc.
Mr Flanagan has said he was "taken aback" by reports that International Trade Secretary Liam Fox is pressurising Prime Minister Theresa May into leaving the European customs union as well as the EU.
Welcoming Mr Brokenshire to Dublin, Mr Flanagan said Ireland does not want to see the UK leaving the customs union.
Insisting the border must remain "invisible", he warned unemployment black-spots that straddle the frontier - such as Derry, Donegal, Fermanagh, Sligo and Leitrim - would be worst hit by a return to border controls.
"It is absolutely essential in my mind that these unique circumstances are taken into consideration, and in this context any return to borders of the past or any imposition of a hard border would adversely impact on the livelihoods of communities in these areas - both north and south," he said.
The European Union customs union is the biggest in the world and countries within it can trade more freely with each other, without tariffs, or taxes on imports.
If Britain were to leave the customs union as well, it would make it more complicated in maintaining a soft border in Ireland.
Mr Fox reportedly wants to leave the customs union to make it easier for Britain to strike new trade deals with non-EU countries after Brexit.