It comes as the party has accused the DUP of betraying the interests of Northern Ireland by agreeing to prop up a Conservative minority government.
The prime minister, he said, has also “just totally ignored the will of the people of Northern Ireland in terms of Brexit”, he added.
Concessions on such issues could seriously damage efforts by the DUP to secure a deal with Sinn Fein to restore Northern Ireland’s devolved government, which collapsed in January.
The party would oppose any deal that would, he said, undermine that agreement.
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.
“Bringing stability to the United Kingdom government in and around issues around Brexit, obviously around counter-terrorism, and then doing what’s right for Northern Ireland in respect of economic matters”.
He told BBC Radio 4’s World at One programme: “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”. It isn’t certain, it is under stress.
“We need to be prepared for the unexpected”.
Sinn Fein’s Michelle Gildernew (Fermanagh and South Tyrone) raised concern about an alliance, saying: “This new arrangement is very unsettling and people are concerned and wary of what it may mean, and what promises will be given or promises extracted from Theresa May”.
Downing Street has warned that direct rule from London could be imposed if no solution is found before the June 29 deadline.
Major warns that a deal could cause the peace process to “unwind”.
While the DUP backed Brexit, it has already stated that it opposes a hard border and wants to maintain the Common Travel Area which would allow the movement of goods and services to go unhindered.
Major said that any DUP deal would inevitably involve giving extra cash to Northern Ireland at the expense of other parts of the UK.
“What we are doing in relation to the productive talks that we are holding with the Democratic Unionist Party is ensuring that it is possible to, with their support, give the stability to the UK Government that I think is necessary at this time”.