The Prime Minister held talks with Arlene Foster, leader of the DUP on Tuesday, with a view to a "confidence and supply" agreement, in which the smaller party would support the Conservatives on budgetary and confidence votes.
Sinn Fein leader Gerry Adams has blasted any deal between the DUP and Conservative Party, saying an alliance would lead to a "coalition of chaos".
Some Tories - including ex-PM John Major - have been alarmed that an arrangement with the DUP would harm the Good Friday Agreement by undermining the United Kingdom government's claim to be impartial.
Former Tory Prime Minister John Major has spoken out against Theresa May's intent to prop up a government with the support of the Democratic Unionist Party (DUP).
It is thought that an announcement on an agreement will be delayed as a result of the Grenfell Tower tragedy - and may not come until next week.
The proposed deal would see the DUP back the Conservatives in votes on the Budget and on any confidence motion while other matters would be negotiated on an issue-by-issue basis.
It could also delay the start of Brexit talks.
Over recent days there has been enormous focus in the national media on the DUP's past opposition to homosexuality, when it led the "Save Ulster from Sodomy" campaign, and its more recent rejection of gay marriage in Northern Ireland.
Trump calling on more restrictions with trade, travel to Cuba
Americans will not be allowed to conduct any business with anyone or entity linked to the Cuban military or intelligence services. Cuban state TV said: "The government of Cuba denounces the new measures toughening the embargo that are destined to fail".
"We're not in any way signing up to the DUP manifesto".
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".
"People knew that we were abstentionist MPs, they have elected us to represent them but not to take our seats". An agreement to restore devolved power-sharing government in Stormont must be reached by the 29 June deadline.
"The context in which the talks process is now being asked to operate could have very serious consequences if there is any suggestion of a back room deal with the DUP".
Mrs O'Neill said she would discuss her concerns with new Irish PM Leo Varadkar the following day.
The Conservatives and DUP are now still continuing talks in order to secure a deal, although reportedly only minor details remain to be ironed out.
Before travelling to the French capital, Mrs May had been leading the talks with the DUP.
It is thought Mrs Foster, despite being a Brexit supporter, could seek assurances from Mrs May that she will pursue a softer exit from the European Union, given Northern Ireland's 56% Remain vote and the DUP's desire not to see a return to a hard border with Ireland.
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