NEW YORK — Frank Pierson, an Academy Award-winning screenwriter whose richly textured work included scripts for ‘‘Cool Hand Luke’’ and ‘‘Dog Day Afternoon’’ and who later became an influential Hollywood leader and mentor, died Sunday in Los Angeles at 87.

His death was announced by the Writers Guild of America, West, of which Mr. Pierson twice served as president. He was also president of the Academy of Motion Picture Arts and Sciences from 2001 to 2005. His family said he died of natural causes after a short illness.

Mr. Pierson had been working as a correspondent for Time and Life magazines in the 1950s when he decided to try screenwriting. By 1958, he had quit journalism and sold his first script to the half-hour anthology show ‘‘Alcoa-Goodyear Theater.’’ He was soon writing and directing full time for film and television, beginning with ‘‘Have Gun — Will Travel.’’

He was nominated for ­Oscars for ‘‘Cat Ballou’’ (1965), a Western with Jane Fonda and Lee Marvin, and the chain-gang drama ‘‘Cool Hand Luke’’ (1967), with Paul Newman. He won, for original screenplay, for ‘‘Dog Day Afternoon’’ (1975), directed by Sidney Lumet.

Mr. Pierson said that he struggled mightily with that script — and he used his struggle as a teaching tool. He told students that he had been unable to capture the essence of the central character, the leader of an inept gang of bank robbers who winds up taking hostages.

He broke through after concluding that the thief, based on a real-life robber and played by Al Pacino, was a pleaser, someone trying in his flawed way to make others happy.

“I’ve never heard anyone speak of their own work more dispassionately and more usefully,’’ said Howard A. Rodman, the vice president of the Writers Guild of America, West.

Part of Mr. Pierson’s legacy is a single irresistible line from ‘‘Cool Hand Luke.’’

“What we’ve got here is failure to communicate.’’ a warden (actor Strother Martin) says to the inmate Luke (Newman).

Luke later uses the line himself, and it has been repeated and remixed in popular culture ever since. The American Film Institute ranked it in 2005 as the 11th-best movie quote.

Frank Romer Pierson was born in Chappaqua, N.Y. When he was 18, his mother, Louise Randall Pierson, wrote a best-selling book based on their family life, ‘‘Roughly Speaking,’’ which was made into a film of the same name in 1945. The story includes the tales of three sons who enlist to fight in World War II.

After serving in the Pacific, Mr. Pierson graduated from Harvard with a degree in cultural anthropology.

He leaves his wife, Helene; a daughter, Eve; a son, Michael; and five grandchildren.

In recent years Mr. Pierson was a consulting producer of the TV series ‘‘Mad Men’’ and ‘‘The Good Wife.’’

In the 1980s, he was a founding writer at the Sundance Screenwriters Lab.

“We all learned from Frank,’’ Michelle Satter, wrote on the Sundance website Monday, ‘‘and when he spoke, it always got very quiet in the room.’’