Ireland's EU commissioner said Dublin would "continue to play tough" over its threat to veto talks about trade after Brexit unless Britain provided guarantees over the border between Northern Ireland and the Republic.

Phil Hogan, the EU's agricultural commissioner, said that Britain, or Northern Ireland at least, should remain in the single market and the customs union to avoid a hard border dividing the island.

"If the UK or Northern Ireland remained in the EU customs union, or better still the single market, there would be no border issue," he told The Observer newspaper on Sunday.

British Prime Minister Theresa May has said Britain will leave the single market and the customs unions after Brexit.

Dublin wants a written guarantee that there will be no hard border between the Republic of Ireland and Northern Ireland.

The European Union has said "sufficient progress" needs to be made on the Irish border, along with two other key issues, before EU leaders can approve the opening of trade talks in the new year at a summit on Dec. 14-15.

Dublin and EU officials say the best way to avoid a "hard border" - which could include passport and customs controls - is to keep regulations the same north and south, but the Northern Irish party that is propping up May's government will oppose any deal that sees the province operate under different regulations to the rest of the United kingdom.

"We will not support any arrangements that create barriers to trade between Northern Ireland and the rest of the United Kingdom or any suggestion that Northern Ireland, unlike the rest of the UK, will have to mirror European regulations," the Democratic Unionist leader Arlene Foster said on Saturday.

Ruth Davidson, leader of the Conservatives in Scotland, said on Sunday that the Irish border was "one of the really difficult bits" of the negotiations.

She said Britain's unique future position as the only country that had left the European Union meant its did not need an "off-the-shelf" solution, although she did not specify how the issue should be resolved.

She said any delay in moving onto trade talks would have serious repercussions for businesses.

"I think that it is really important that we get the transitional deal nailed down; that's not for government, that's for businesses so they know what they are doing next year and they are able to plan," she said.

"If we don't make it through in the next two weeks to move onto that next phase, then we are rapidly going to run out of time in terms of getting us to a good position at the time that transitional deal is supposed to take place."