Sinn Fein's Stormont leader Michelle O'Neill said: "I will be making it very clear that any deal between the Tories and the DUP can not be allowed to undermine the Good Friday and subsequent agreements".
Concerns have been raised, including by Sir John Major, that the Government can no longer be the necessary "honest broker" in talks in Northern Ireland, if it is formerly allied with the DUP.
The Tories need the support of 10 DUP MPs to form the government in the United Kingdom after they failed to win a majority in the general elections.
However the announcement of any deal between the DUP and the Conservatives has been postponed due to the London tower block fire.
Under the proposed deal, the DUP would likely support May's Conservatives on big issues such as the budget, Brexit and defence legislation on a vote-by-vote-basis.
May has dismissed calls to resign following the dismal election result after calling a vote three years early in the hope of bolstering her slim majority, only to actually lose seats.
If the announcement of the deal is delayed, then the Queen's speech, which is supposed to happen on Monday, June 19, could also be delayed by at least a week. The former prime minister Sir John Major has suggested it will be hard for the government to act as an honest broker in talks to restore the power-sharing agreement in Belfast if it enters into a deal with the DUP to prop up a Conservative minority government in Westminster.
"It's going to be hard".
Prime Minister Theresa May wants to negotiate the divorce and the future trading relationship with the European Union before Britain leaves in March 2019, followed by what she calls a phased implementation process to give business time to prepare for the impact of Brexit.
While the DUP continue to hammer out the details of the arrangement with the Tories, the other four main parties at Stormont confirmed they would be meeting Mrs May on Thursday.
"Yesterday Emmanuel Macron, the new French president, spoke about an open door, he said if Britain is changing its mind it will find an open door", Verhofstadt told the European Parliament.
"It's a unity of goal, having voted to leave the European Union, that their Government gets on with that and makes a success of it, and we are committed to developing a deep and special partnership with the EU".