"I am dubious about it", Major told BBC radio.
"We have seen in Northern Ireland over very many years that events always don't unwind as you expect them to unwind", he said.
They are hoping to ramp up the pressure on the region's largest political party to change its stance at a time when its policies on social issues are under renewed scrutiny due to the likely parliamentary deal with the minority Tory government.
SPUC CEO John Smeaton added: "The pro-life and pro-family citizens of Britain and Northern Ireland will not be silenced by the vicious attacks on the pro-life and pro-family values of Northern Ireland MPs who are now in the spotlight as Theresa May seeks to form a government with their support".
Abortions are only permitted in Northern Ireland if a woman's life is at risk or if there is a permanent or serious risk to her mental and physical health.
Major, who helped lay the foundations of the 1998 agreement that ended two decades of sectarian conflict in Northern Ireland when he was in government, said it would imperil the United Kingdom government's impartial role in the peace process. It is equally if not more vital to remember that the peace process is just that - a process, ongoing and by no means complete - a process which your Government are co-guarantors of via the Good Friday Agreement.
"The last thing anybody wishes to see is one or other of the communities so aggrieved that the hardmen, who are still there lurking in the corners of the communities, decide that they wish to return to some form of violence".
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Northern Ireland is the only part of the British Isles where same-sex marriage remains outlawed.
Following March's snap Assembly election, the DUP no longer has the electoral strength to deploy a petition of concern in its own right, though it could still potentially combine with other socially conservative MLAs to do so.
He was referencing efforts to maintain the independence of Austria but similar could be said of successive UK Governments' general attitude towards Northern Ireland and the dismal record of human rights violations that persists there to this day.
"We need to be prepared for the unexpected". She said the two parties have "had some very good discussions" and both sides want to bring "stability to the UK Government".
The Prime Minister held talks with Arlene Foster, leader of the DUP on Tuesday, with a view to agreeing a "confidence and supply" agreement, in which the smaller party would support the Conservatives on budgetary and confidence votes.
He joked that he welcomed the prospect of a Queen's Speech once this "coalition of chaos has been negotiated", but said if this did not happen, he was "ready to offer strong and stable leadership in the national interest".
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