Commenting on the proposed DUP-Conservative deal, Sinn Féin MP Elisha McCallion said her party's priority was "defending the Good Friday Agreement, protecting our public services and establishing an executive based on equality and respect".
The leader of Northern Ireland's DUP has said that it is "complete and utter nonsense" to describe her party as homophobic.
Downing Street insisted tomorrow's talks will focus on restoring the Stormont Assembly.
"We stand at a critical time with those Brexit negotiations starting only next week - I think that stability is important".
An announcement on an agreement may not come until next week as it is thought it will be delayed as a result of the Grenfell Tower tragedy.
For Labour, shadow business secretary Rebecca Long-Bailey said the prospect of a Conservative-DUP deal was "worrying", telling BBC Radio 4's Today programme: "It would create a lot of instability in terms of the peace process in Northern Ireland".More news: Brian Harman takes US Open lead after day three
And despite French President Emmanuel Macron stating the United Kingdom could still opt to remain an European Union member, Verhofstadt added this would not mean a return to previous circumstances.
DUP leader Arlene Foster arrived for talks with May.
Sources say delay over Govt deal with DUP not cos talks are "stuttering" - 95% agreed between both sides.
As European leaders tried to fathom exactly how Britain would begin the negotiations, German Finance Minister Wolfgang Schaeuble said Germany wanted a Brexit deal that would limit negative consequences for the bloc but also did not want it to weaken Britain.
Almost a fifth of the UK's food and drink exports go to the Republic of Ireland and in March industry bodies from across the British food and drink sector wrote an open letter to various government departments calling for "frictionless" tariff-free trade with Ireland to continue post-Brexit.
London's neutrality is key to the delicate balance of power in Northern Ireland, which was once plagued by violence over Britain's control of the province.More news: Congressional Baseball Game carries on, one day after shooting
After days of uncertainty, the Government announced that the State Opening would now take place on Wednesday June 21 - two days later than originally scheduled.
"She said: "I'm the person who got us into this mess and I'm the one who is going to get us out of it", said one Conservative lawmaker who attended Monday's meeting.
Mrs May held talks at Downing Street with the other Northern Ireland political parties in an attempt to allay growing concerns that the expected DUP deal would undermine the peace process.
Colin Talbot, a professor of government at the University of Manchester, said the Paris trip is part of May's strategy to improve her position at home.
While the DUP are deeply eurosceptic, they have baulked at some of the practical implications of a so-called hard Brexit, including a potential loss of a "frictionless border" with the Republic of Ireland.More news: LeBron James: Cleveland Cavaliers will continue building toward NBA Championship
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