Built like a truck but with the capacity to be as gentle as a pussycat, Brian Dennehy was smarter than the average bear-like character actor. The 6ft 3in performer, who has died aged 81 from a heart attack resulting from sepsis, made his screen breakthrough as an adversarial small-town sheriff in First Blood (1982), the thoughtful opening instalment in what would become the Rambo action series. It was the first in his hat-trick of hits from that decade: he also twinkled benignly as one of a group of aliens who have a rejuvenating effect on an elderly community in Cocoon (1985) and played a grizzled but amiable cop in F/X (1986), an enjoyable thriller set in the special effects industry; it was popular enough to spawn a 1991 sequel in which he also starred.

Unusually for a character actor, he had a handful of movie leads, including The Belly of an Architect (1987), a rare foray into arthouse cinema. Dennehy’s extraordinary range, from cowering vulnerability to a fury fit to scare the gods, was given full rein in the British director Peter Greenaway’s otherwise austere tale of an esteemed architect dying of stomach cancer; the critic Janet Maslin called it “one of the best things” the actor had done. He also gave a complex and probing performance as the serial killer John Wayne Gacy in the TV mini-series To Catch a Killer (1992).

Facebook Twitter Pinterest Brian Dennehy, right, in his breakthrough role in First Blood, 1982, with Sylvester Stallone as Rambo. Photograph: Thorn EMI Video/Joseph Lederer/Visual Icon

It was on stage, however, that Dennehy established himself as a genuine colossus and one of the US’s foremost tragedians. He won Tony and Olivier awards for playing Willy Loman in the New York and London productions of Death of a Salesman (in 1999 and 2005 respectively), as well as a Golden Globe and a Screen Actors Guild award for the 2000 television version. “You can play Willy as a little man with big ideas,” wrote Michael Billington in his review of the Lyric theatre production, “but what Dennehy gives us is a physical giant facing up to his own vulnerability.”

His second Tony, in 2003, was for Long Day’s Journey Into Night, in which he starred opposite Vanessa Redgrave and the late Philip Seymour Hoffman; it was directed, as Death of a Salesman had been, by his friend and collaborator Robert Falls, whom he called “the person who’s had the greatest effect on my life”. Falls also directed him twice in another Eugene O’Neill masterpiece, The Iceman Cometh, first in 1990 with Dennehy as the charismatic lead, Hickey, and then in 2012 with him playing the sloshed “Foolosopher” and former anarchist Larry Slade; both productions originated, like much of their work together, at the Goodman theatre in Chicago. Preparing for the most recent one, he said: “The only way to do it is to grab the fuckin’ audience by the throat, shake the shit out of ’em and say, ‘You think you’re getting out of here alive? You’re not. Prepare to spill your fucking blood, because I’m gonna spill mine, and you’re coming with me.’”

O’Neill’s work was vital to any understanding of Dennehy – Falls also directed him in productions of Hughie, A Touch of the Poet and Desire Under the Elms – and he claimed to concur with the playwright’s mordant, ravaged vision. “Except in terms of my kids and my grandchildren and my wife, it’s pretty hard not to look outside yourself and feel bleak. I’m not as dark as O’Neill, thank God. But I have my dark moments.” His own personality flowed freely into those performances. “Falls always says that I have more rage than any person he’s ever known … Tragic acting involves going to those places, places that do actually exist in yourself. I don’t have any trouble tapping into them.”

He was an intemperate drinker, describing himself as a former “functioning alcoholic”, and once joked: “At my parties, the sheriff’s department comes three or four times a night.” But it was his background that helped make him an ideal interpreter of O’Neill. “It’s pretty self-evident for me. Irish Catholic, lapsed Catholic, whatever the hell you want to call it. Somebody who’s definitely gone 15 rounds with the booze, and wound up with a lot of black eyes and broken teeth as a result of it.”

He was born in Bridgeport, Connecticut, and raised first in Brooklyn, New York, and then, from the age of 12, in Mineola, Long Island, by his parents Hannah (nee Manion) and Edward Dennehy, a correspondent for the Associated Press. He was educated at Chaminade high school, where a teacher encouraged him to pursue a career in acting. He chose sport instead and went to Columbia University on a football scholarship before joining the Marines. He told the New York Times in 1989 that he had incurred shrapnel injuries in Vietnam. When it later emerged that he hadn’t served there at all, he apologised for fabricating his record.

Facebook Twitter Pinterest Brian Dennehy in Dynasty, with Joan Collins as Alexis, 1981. Photograph: ABC Photo Archives/Walt Disney Television via Getty Images

After the Marines, he completed a graduate degree in dramatic arts at Yale and then worked as a delivery driver, a butcher, a bartender and a stockbroker. In the early 1970s he decided to give acting a concerted shot after several years of community theatre in Long Island. Stage roles in New York led eventually to minor parts in movies, beginning with Looking for Mr Goodbar and Semi-Tough (both 1977), and on TV in the likes of Kojak, M*A*S*H, Dallas and Dynasty. His film work became increasingly memorable: he played a consoling bartender in the Dudley Moore comedy 10 (1979), a father whose son joins a cult in Split Image (1982), a cop moonlighting as an author in Best Seller (1987), a corrupt district attorney in Presumed Innocent (1990) and Romeo’s father in Baz Luhrmann’s modern-dress Romeo + Juliet (1996). Notable theatre credits include the title role in Brecht’s Galileo in 1986 at the Goodman theatre (his first play with Falls) and Lopakhin in Peter Brook’s revival of The Cherry Orchard at the Brooklyn Academy of Music in 1988.

Dennehy worked relentlessly throughout his career. He appeared in a series of TV movies, five of which he also directed, as the Chicago cop Jack Reed, beginning with Deadly Matrimony (1992). Recently he had recurring roles on television in Public Morals (2015) and The Blacklist (2016—19).

He is survived by his wife, the costume designer Jennifer Arnott, whom he married in 1988, and by their children, Cormac and Sarah, as well as by three daughters, Elizabeth, Kathleen and Deirdre, from his first marriage to Judith Scheff, which ended in divorce in 1974.

• Brian Manion Dennehy, actor, born 9 July 1938; died 15 April 2020