The First Minister has urged the UK Government to "stand up" to their Brexit commitments.
Arlene Foster conceded she does not like the Northern Ireland Protocol, which will see UK authorities apply EU customs rules to goods entering the region, but has accepted it is a "legislative reality".
She was speaking as Cabinet Office minister Michael Gove tried to reassure Northern Ireland MPs that the UK Government is seeking a deal with the EU which protects their constituents.
Mrs Foster said the UK Government must "stand up" to commitments made in its command paper.
Some unionists have expressed concerns that the protocol creates a border down the Irish Sea.
Mrs Foster was challenged over accepting the protocol at Stormont yesterday by TUV leader Jim Allister.
"Does she no longer fear or think that it will create constitutional and economic damage of a catastrophic nature?" he asked.
The First Minister responded: "There is not much point in standing and saying we don't accept the protocol, when the protocol is legislative reality.
"I may not like it, I don't like it, let's be very clear about that.
"But my job now as First Minister is to try and make sure that we minimise any checks between Great Britain and Northern Ireland, because obviously there are checks at the moment, SPS checks (to protect against disease, pests and contaminants) between Great Britain and Northern Ireland, but we have to make sure that those are kept to a minimum. We must make sure that there is unfettered access, as it says in the UK Government command paper.
"We will, very much, want to see the government standing up to what their commitments are in the command paper."
Mrs Foster also responded to a question from Sinn Fein MLA Catherine Kelly, asking for an update on the implementation of the protocol. She said that work is under way on aspects within Stormont's remit, such as agri-food requirements.
Yesterday in the House of Commons, the DUP's Carla Lockhart asked what further progress has been made on ensuring there will be no additional declaration forms needing to be completed when sending goods from Northern Ireland to Great Britain.
"They will have unfettered access to the rest of the UK," Mr Gove said.
North Down Alliance MP Stephen Farry asked Mr Gove: "Does the minister realise that in the event we fail to secure a deal with the European Union, and the government opts to trade on its terms, then the impact of a border down the Irish Sea would be more severe, with businesses facing more costs and households too?"
Mr Gove replied: "It is the case that we will push to secure a deal and a deal would be in everyone's interests."