The party has warned they could withdraw their support for the Conservatives
The DUP have threatened to withdraw from the 'confidence and supply' arrangement that is propping up the British Government over the Irish border issue.
The party has warned British Prime Minister Theresa May that she may not be able to count on their votes, if she agrees to any Brexit solution that places barriers, "real or perceived" between the North and Britain.
The party's arrangement with the Conservatives has seen them voting as one on major legislation including the Queen's Speech, the Budget and Brexit.
However, the agreement does not cover the precise outcome of the EU divorce deal.
Both the Irish Government and the EU have consistently warned that Brexit negotiations cannot move on to the next phase until "sufficient progress" is made on the border issue.
All sides have insisted that there can be no return to a hard border, and the Taoiseach Leo Varadkar has made it clear that Ireland will block the talks from moving forward unless a solution is “written down in practical terms in the conclusions of phase one."
Ireland has called for a solution that would keep the North within the customs union - thus negating the need for a border.
However, the British Government has insisted that the UK will leave both the customs union and the single market - while the DUP has said it will not accept any solution that keeps the North within either arrangement while the rest of the UK remains without.
There has been some speculation that the British Government was considering some form of "regulatory convergence" between the North and the Republic that would break the deadlock, however this afternoon the DUP warned they would look to block any such proposal.
DUP Party officials have suggested they view convergence as tantamount to keeping Northern Ireland within the customs union - thus creating a new unofficial border between Northern Ireland and the UK.
They have insisted this would be unacceptable, with one senior official claiming it could prove "deeply destabilising" to the confidence and supply agreement with the Conservatives.
In a statement this afternoon, DUP Arlene Foster claimed the UK had voted to leave the EU as one nation adding, "we are leaving as one nation."
In fact, both Northern Ireland and Scotland voted to remain in the EU by margins of 55.8% and 62% respectively.
Mrs Foster went on to say that her party "will not countenance any arrangement that could lead to a new border being created in the Irish Sea."
"We are in constant contact on these issues with the Government and during our discussions, we reiterated that United Kingdom–Republic of Ireland arrangements may be necessary as we exit the EU," she said.
"But there can be no arrangements agreed that compromise the integrity of the UK single market and place barriers, real or perceived, to the free movement of goods, services and capital between Northern Ireland and the rest of the United Kingdom."
She said her party supports the continuance of the Common Travel Area allowing people to move freely between the North and the Republic.
UK and EU officials are expected to work through the weekend in an attempt to hammer out an agreement that heads off the threat of any return to a hard border.
Reports from Brussels suggest five written commitments have been drafted for the UK to sign up to before negotiations are permitted can move to phase two.
The European Council President Donald Tusk is due to meet the Taoiseach in Dublin tomorrow ahead of what will be an extremely busy weekend.
He is due to meet with Theresa May on Monday.