The former Conservative prime minister told the BBC on Tuesday afternoon he was "concerned", "wary" and "dubious" about the proposed agreement.
A deal between the DUP and the Conservatives was delayed amid the response to the London fire tragedy.
Mrs May needs the votes of the DUP's 10 MPs to prop up her minority administration.
"It's imperative that both governments recommit to the word, spirit and implementation of the Good Friday Agreement if there is to be any prospect of re-establishing the Executive. And we can not know if that impartiality is going to be crucial at some stage in the future".
By forming a government with the DUP, many commentators have argued the Conservatives would undermine this arrangement and risk the peace process. People shouldn't regard it as a given. "It isn't certain, it is under stress".
"If there are difficulties with the Northern Ireland executive or with any one of a number of things that might well arise during the Brexit negotiations, it's very important that there's an honest broker - and the only honest broker can be the United Kingdom government", Major said. "We need to hope for the best but prepare for the worst", he said.
"The last thing anybody wishes to see is one or other of the communities so aggrieved that the hard men, who are still there lurking in the corners of the communities, decide that they wish to return to some form of violence".
SDLP Leader Colum Eastwood said: "The context in which the talks process is now being asked to operate in could have very serious consequences if there is any suggestion of a back room deal with the DUP".More news: Israeli policewoman stabbed to death in Jerusalem
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He added: "The UK government is offering whatever support we can, working alongside the Irish government, as appropriate, honouring our respective commitments in the Belfast Agreement to serve the interests of the whole community in Northern Ireland".
He did not expect the peace process to "collapse" suddenly, but Sir John cautioned: "I think we have to take care with it and take care that everything we do does not exaggerate the underlying differences that still are there".
The DUP have been playing their cards close to their chest, but we know the areas they're talking about because of a DUP plan drawn up in 2015 in anticipation of a hung Parliament.
"Ultimately, I think the parties understand people voted in the March Assembly elections for a strong voice at Stormont".
May's authority has been severely diminished after a disastrous general election which saw her lose her Commons majority.
But the other Stormont parties have warned that any deal between the DUP and Conservatives could make restoring power sharing more hard.
It comes after May told Tory MPs last night: "I'm the person who got us into this mess and I'm the one who will get us out of it".