Hurt won the best actor Oscar in 1986 for playing a prisoner in a Brazilian jail in Kiss of the Spider Woman.
He was nominated two more times in the next two years, for Children of a Lesser God and Broadcast News.
In recent years, he has been known as General Thaddeus “Thunderbolt” Ross in five Marvel blockbusters.
Hollywood website Deadline quoted a statement from Hurt’s son Will as saying: “It is with great sadness that the Hurt family mourns the passing of William Hurt, beloved father and Oscar winning actor, on March 13, 2022, one week before his 72nd birthday.
“He died peacefully, among family, of natural causes. The family requests privacy at this time.”
Variety said the news was confirmed by Hurt’s friend Gerry Byrne.
Fellow Marvel actor Mark Ruffalo wrote on Twitter: “Wow, another Major loss to the acting community. Great actor. Great mind. RIP.”
Matthew Modine described him as “a consummate professional” who was “continually searching for greater truth and human understanding”.
Antonio Banderas said “a great actor has left us”, while other tributes came from Russell Crowe, M Night Shyamalan Rebecca Front.
Hurt began acting on stage in the 1970s before making his big-screen breakthrough as an obsessed scientist in Altered States, which earned him a best newcomer nomination at the Golden Globes in 1981.
That year, he also starred as a womanising lawyer in erotic thriller Body Heat, before being cast in The Big Chill and Gorky Park.
Winning an Oscar for playing a gay man who shares a cell with a political prisoner in Kiss of the Spider Woman was “very isolating”,he later told the Los Angeles Times.
“The instant they gave it to me, I thought, God, what do I do now? How am I going to walk into a room and have any other actor trust me?”
That did not stop him getting two more consecutive nominations, though, before roles in The Accidental Tourist, Lost in Space, Contagion and AI. Then came a fourth Oscar nomination for David Cronenberg’s A History of Violence in 2006.
He also received Emmy nominations for playing Treasury Secretary Henry Paulson in 2011’s Too Big to Fail, and for legal TV drama Damages.
He returned to the theatre in productions including Henry V, A Midsummer Night Dream and Hurlyburly, the latter of which saw him recognised with a nomination at Broadway’s Tony Awards.
He was regarded as a compelling but complex and often confrontational presence, however. Fame was “a challenge” and “not a happy condition for me”, he admitted.
“It’s a privilege and a responsibility, and I’m not sure I carried the responsibility well at times, which is embarrassing,” he told The Telegraph in 2013. “And I’ve had to look and be disappointed in myself occasionally for how I behaved in some circumstances.”
He drank heavily for a spell and in a high-profile palimony trial in 1989, former partner Sandra Jennings described his drunken rages.
Another former girlfriend, Children of a Lesser God co-star Marlee Matlin, later accused him of physical and emotional abuse. He apologised “for any pain I caused”.
The actor revealed in 2018 that he had been diagnosed with terminal prostate cancer.