NEW YORK — Liam Cosgrave, a dour and dogged former prime minister of Ireland whose ingrained devotion to political stability in the 1970s helped break his country’s cycle of violence, died on Wednesday in Dublin. He was 97.

His death, in a hospital, was confirmed by Leo Varadkar, the prime minister of the Republic of Ireland. He said that Mr. Cosgrave had “always believed in peaceful cooperation as the only way of achieving a genuine union between the people on this island.’’

Mr. Cosgrave’s law-and-order agenda and renunciation of terror were steeped in his own family’s protracted revolt against British domination since the Irish Rebellion of 1798.

His father, W.T. Cosgrave, participated in the 1916 Easter Rising and was sentenced to death for his role in it, though the sentence was commuted to a life term, which in turn was nullified when he was released in 1917.

The elder Cosgrave was the first elected president of the executive council of the Irish Free State, serving from 1922 to 1932. The post was considered equivalent to the prime minister.

Liam Cosgrave was a member of the Dail Eireann, or Assembly of Ireland, from 1943, when he was 23, until 1981 and led the Fine Gael party from 1965 to 1977. He was elected prime minister in 1973, but an economic slump helped doom his chances for reelection four years later.

During his one term in office, he negotiated what became known as the Sunningdale Agreement, which diluted the Irish Republic’s constitutional claim to Northern Ireland. The agreement signed by the mostly Roman Catholic republic acknowledged that the predominantly Protestant north was a province under British control.

Both sides agreed that the status of the six counties that constituted Northern Ireland could change but only by a majority vote of their residents.

While the agreement collapsed within months, it formed the basis for the 1998 Good Friday power-sharing arrangement that eventually ended years of sectarian violence in Northern Ireland, commonly known as the Troubles. Seamus Mallon, a Northern Irish minister, described the Good Friday Agreement as “Sunningdale for slow learners.’’

On a trip to Washington in 1976, Mr. Cosgrave, addressing a joint meeting of Congress on St. Patrick’s Day, characterized Americans who financed terrorists in British-ruled Northern Ireland as “people who support violence at a distance and who can sleep easy on the wounds of others.’’

Later that year he pressed for the imposition of legal restraints on the Irish Republican Army, which fought to make all of Ireland an independent republic, saying: “The crimes perpetuated by men of violence have brought discredit to the name of Irishmen throughout the world and death and damage to our own people. Our past has been devalued and our future threatened by their outrages.’’

Liam Cosgrove was born on April 13, 1920, in Castleknock, a Dublin suburb, just months before the establishment of the Irish Free State that year — “Year One in Irish history,’’ as the dramatist Sean O’Casey wrote.

His mother was the former Louisa Flanagan. His father, William, was a grocer and pub keeper who was elected to the first Irish Assembly in 1919 after his release from prison. He became head of the provisional government in August 1922 after the deaths of Michael Collins and Arthur Griffith, both of whom helped negotiate the Anglo-Irish Treaty, and he dealt ruthlessly with the new administration’s opponents.

Liam Cosgrave interrupted his law studies at the Honorable Society of King’s Inns, a school in Dublin, to protect Irish neutrality during World War II. He was commissioned a lieutenant in the Defense Forces and admitted to the bar in 1943, the year he began serving in the Assembly with his father.

His wife, the former Vera Osborne, died in 2016. He leaves three children, Mary, Liam T., and Ciaran, and two grandchildren.

In 1970, Mr. Cosgrave was instrumental in pressuring Prime Minister Jack Lynch to fire two ministers accused of importing arms for the Irish Republican Army.

A staunch Catholic, Mr. Cosgrave stunned his party colleagues in 1974 by opposing his own government’s bill that would have allowed married couples to obtain contraceptives. The bill was defeated.

An ardent horse breeder and fox hunter, he presided over a relatively progressive government.

“Cosgrave’s strength,’’ the Irish writer Conor Cruise O’Brien said in 1986, “and the limiting factor on his strength, was his very strong emotional attachment to the institutions of this state, and his hostility to anything that might overthrow or damage them.’’