The British Prime Minister also warned republicans were wrong if they believed that Britain was suffering from “battle fatigue”.
According to an Irish Government memo, the British Prime Minister made the comments at meeting in Downing Street in February 1992, where he hosted newly- elected Taoiseach Albert Reynolds and senior Irish ministers.
The meeting, which came weeks before the UK general election, was held amid the backdrop of ongoing talks between the main political parties in Northern Ireland.
At the meeting, the Taoiseach asks Mr Major directly: “Do you think we can defeat the IRA?”
He responds: “Militarily that would be very difficult. I would not say this in public, of course, but, in private, I would say, possibly no.”
The memo reveals the frustrations both sides felt regarding a lack of progress in talks between the main political parties, while also revealing early efforts on the Irish side to push for the inclusion of Sinn Fein in any negotiations on a future settlement.
“My own impression is that the talks are not getting anywhere,” Mr Reynolds said.
The Prime Minister, referring to the Secretary of State for Northern Ireland, says: “Peter Brooke thinks they have some life.”
Mr Reynolds responds: “I would say that here … but not outside.”
The Irish leader tells the Prime Minister that he believes the IRA are “serious” about peace.
Several days earlier, Sinn Fein had published a document called Towards a Lasting Peace in Ireland.
Mr Major, according to the Irish memo, said: “If we pursue that, we could run into very serious opposition here. You know that more bombs are threatened in Whitehall. If they are serious, they are certainly going the wrong way about it.”
The IRA had attacked 10 Downing Street during a Cabinet meeting the previous year.
Mr Major continues: “They will not get peace by putting bombs in Whitehall – rather the opposite. Why do they behave as they are now behaving if they want peace?”
Mr Reynolds tells the British Prime Minister “they always do that”.
“Before a cessation of violence, they always become more active,” he said. “They always like it to appear that if a ceasefire comes about, then they have not acted from weakness.”
Mr Reynolds then asks, appearing to refer to the Sinn Fein text: “Is there any way in which we could look at the language, with a view to moving things along?”
Mr Major says: “I know Gerry Adams and one or two others are involved in this. They think we are suffering from battle fatigue. They’re wrong. They could be engaged in a very cynical game.”
At the meeting, Mr Reynolds says he believes “peace may well be in sight”.
In a frank assessment of the current situation in Northern Ireland, the Taoiseach warns the two governments are dealing with “a divided community”.
He said: “We must draw up structures to accommodate these differences; and these structures must command confidence.””