BOSTON — A federal judge yesterday ordered the government to pay more than $101 million in the case of four men who spent decades in prison for a 1965 murder they didn’t commit after the FBI withheld evidence of their innocence.

The FBI encouraged perjury, helped frame the four men, and withheld for more than three decades information that could have cleared them, U.S. District Judge Nancy Gertner said in issuing her ruling yesterday. She called the government’s argument that the FBI had no duty to get involved in the state case “absurd.”

Peter Limone, Joseph Salvati, and the families of the two other men who died in prison had sued the federal government for malicious prosecution. They argued that Boston FBI agents knew mob hitman Joseph “The Animal” Barboza lied when he named the men as killers in the 1965 death of Edward Deegan. They said Barboza was protecting a fellow FBI informant, Vincent “Jimmy” Flemmi, who was involved.

The four men convicted on Barboza’s lies were treated as “acceptable collateral damage” because the FBI’s priority at the time was taking down the Mafia, their attorneys said.

A Justice Department lawyer had argued that federal authorities couldn’t be held responsible for the results of a state prosecution and had no duty to share information with the officials who prosecuted Mr. Limone, Mr. Salvati, Henry Tameleo, and Louis Greco.

“The FBI’s misconduct was clearly the sole cause of this conviction,” the judge said yesterday. “The government’s position is, in a word, absurd.”

“No lost liberty is dispensable. We have fought wars over this principle. We are still fighting these wars,” Judge Gertner told the packed courtroom.

Mr. Salvati and Mr. Limone were exonerated in 2001 after FBI memos dating back to the Deegan case surfaced, showing the men had been framed by Barboza. The memos were made public during a Justice Department task force probe of the FBI’s relationship with gangsters and FBI informants James “Whitey” Bulger and Stephen “The Rifleman” Flemmi. Mr. Limone, now 73, and Mr. Salvati, 75, stared straight ahead as the judge announced her ruling. A gasp could be heard from the area where their friends and family were sitting when Judge Gertner said how much the government would be forced to pay. The men’s attorneys had not asked for a specific amount in damages, but in court documents they cited other wrongful conviction cases in which $1 million was awarded for every year of imprisonment. Judge Gertner ordered the government to pay $101.7 million.

“Do I want the money? Yes, I want my children, my grandchildren to have things I didn’t have, but nothing can compensate for what they’ve done,” Mr. Salvati said.

Mr. Salvati had been sentenced to life in prison as an accessory to murder and served more than 29 years before his sentence was commuted in 1997.

“It’s been a long time coming,” Mr. Limone, who served 33 years in prison before he was freed in 2001, said. “What I’ve been through — I hope it never happens to anyone else.”