Although the DUP are unionists - wanting to remain part of the United Kingdom - and broadly support numerous policies of the Conservative and Unionist Party (as the Conservatives are correctly called), May's proposed deal could scupper attempt to broker a power-sharing deal with Sinn Fein - which promotes the unification of Ireland - on the Northern Ireland Executive.
"But time is running short and the parties must come together by the June 29th for the return of a strong voice at Stormont and for a brighter future for everyone in Northern Ireland".
The party would oppose any deal that would, he said, undermine that agreement.
Voters in Northern Ireland who support the reunification of the island are now without representation in the British parliament.
Sinn Féin, he said, "won't interfere in British affairs".
"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".
It had been hoped May and DUP leader Arlene Foster would reach an agreement Wednesday that would give the Conservatives a small working majority.
"Speaking with the parties today, it was clear that real progress was made in the last round of discussions and agreement can be reached if there is good will on all sides".
London highrise fire: 58 missing, presumed dead, police say
Cundy said there may have been other people in the tower who police are not aware of, and that could increase the death toll. That includes those who we believe died here at Grenfell tower , and those who are in critical care still in hospital.
He added: "The danger is that however much any government tries they will not be seen to be impartial if they are locked into a parliamentary deal at Westminster with one of the Northern Ireland parties".
Labour leader Jeremy Corbyn yesterday accused Mrs May of embarking on a "coalition of chaos" with the DUP.
"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, and we are committed to developing a deep and special partnership with the European Union".
Mr Adams said his party will not take its seats in Westminster or swear an oath to the Queen, joking: "No harm to her".
"We have worked as a party with the DUP before and those are productive talks. So of course we would support any monies going to the executive", Adams said.
Sir John - who had remained silent during the six-week election campaign - is "concerned" about the impact a deal could have on politics in the province.
A DUP source told the Guardian the deal was 95 percent agreed but that the Grenfell Tower fire in London would likely delay any formal announcement of the pact.
He claimed such a deal could endanger the peace process.
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