Meanwhile, a deadly fire at a tower block in London could delay the announcement of any deal to stay in power, the BBC reported.
Sinn Fein, the SDLP and Alliance have all made clear Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore powersharing at Stormont due to their perception he has a conflict of interest.
Martin Mansergh, a key negotiator of the Good Friday Agreement, said he did not necessarily share the concerns expressed by former Prime Minister John Major and others that a deal between the DUP and Tory administration could harm the peace process.
They discussed the outcome of the United Kingdom general election and Mrs May outlined the proposed supply and confidence arrangement with the DUP.
It comes as the party has accused the DUP of betraying the interests of Northern Ireland by agreeing to prop up a Conservative minority government.
"Northern Ireland's political leaders now have it in their hands to take control and shape a brighter future for everyone in Northern Ireland".
Ministers have already said that the Queen's Speech may have to be set back from its scheduled date of next Monday June 19 because of the ongoing negotiations.
But May's predecessor, David Cameron, said there would be pressure after last week's surprise for a "softer" Brexit that gave greater priority to a close trading deal with the EU.
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Despite the uncertainty over her ability to govern, May had confirmed that Brexit negotiations - expected to be the most complex worldwide talks Britain has held for decades - would begin as planned next week.
Sinn Fein said that it was important there was transparency over any deal between the Conservatives and the DUP, and that compromises over certain policy areas could hinder efforts to form a new Northern Irish executive.
"It's going to be hard".
That would help safeguard jobs and trade with European Union members but would severely restrict the UK's ability to strike its own trade deals around the world.
But speaking during a visit to Paris to meet French president Emmanuel Macron, Mrs May told reporters: "We as Government remain absolutely steadfast in our commitment to the Belfast Agreement and the subsequent agreements and we continue to work with all the parties in Northern Ireland and the Republic of Ireland in ensuring that we can continue to put in place those measures necessary to fulfil those agreements".
Mrs May stressed Brexit would happen and the timetable remains on course.
Sky sources said earlier there had been "slower progress" in talks between the Tories and the DUP, with an agreement unlikely to be announced on Wednesday.
"It's a unity of objective, having voted to leave the European Union, that their government gets on with that and makes a success of it".
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