Northern Ireland, along with Scotland and Wales should expect a "significant increase" in powers for their administrations post-Brexit, David Davis has said.
The Brexit Secretary was pressed by Labour to guarantee that the UK's withdrawal from the EU would not be used as an "excuse to hoard powers in Whitehall".
Mr Davis gave the assurance to the devolved nations as he outlined how the Westminster Government intends to oversee the conversion of EU law onto the UK statute.
The Tory frontbencher also asserted the importance of keeping the UK's internal market together in the face of renewed calls for another Scottish independence referendum.
Speaking in the Commons, shadow Brexit secretary Sir Keir Starmer said: "Brexit should not be an excuse to hoard powers in Whitehall.
"There has to be a heavy presumption that devolved matters remain devolved as powers and responsibilities transfer from the EU to the UK."
Mr Davis, in his reply, said: "No powers currently exercised by them will be taken away. We've said that time and again.
"We also expect there to be a significant increase in the powers exercised by the devolved administrations.
"But I say this - we have to maintain the United Kingdom internal market too.
"That is four times as important to Scottish businesses, for example, as the European market.
"It's incredibly important to Northern Irish and Welsh businesses too, and the administrations understand that.
"But we will be having discussions with them at length - we've already started - about how we exercise this, and I'm very happy to talk to him directly about the matter if that is useful to him."
David Davis said the Government does not know if the UK's devolved institutions will need to sign off law changes made through the so-called "Great Repeal Bill".
Devolved institutions give permission to the UK Parliament to pass laws relating to devolved matters by agreeing a legislative consent motion.
But the Brexit Secretary said ministers "don't know" yet if permission will be needed as the UK looks to convert EU law into UK law.
SNP frontbencher Joanna Cherry said: "Yesterday, Mr Speaker, you invited me to behave as if I was in a court of law.
"Can I extend your entirely appropriate invitation to the Secretary of State and suggest that he pretend that he is in a court of law and answer the question posed by my honourable friend, the member for North East Fife (Stephen Gethins): Will this Bill require legislative consent motions, yes or no?"
Mr Davis replied: "I actually apologise - I forgot the point that he (Mr Gethins) was making in terms of responding to the other ones.
"At this stage we don't know because we don't know the final format of the Bill.
"That's the simple truth."
