Bedeviled for over 34 years by the mysterious killing of Olof Palme, the Swedish prime minister who was shot in the back by an unknown assailant on a quiet Stockholm street, Sweden’s judiciary finally made its case on Wednesday.

At a news conference in Stockholm, the prosecutor Krister Petersson said that there was “reasonable evidence” that the assailant was Stig Engstrom, a graphic designer at an insurance company, who killed himself in 2000, at the age of 66. He added that only a court could rule on whether Mr. Engstrom was guilty or not, but that since the suspect is deceased, there would be no court case.

But the prosecutor said he could not rule out the possibility that Mr. Engstrom had acted as part of a larger conspiracy.

Mr. Palme was killed on a cold February night in 1986 after leaving a movie theater in Stockholm with his wife, Lisbeth. The assassination shocked Sweden and evolved into one of the country’s greatest mysteries.

He was a liberal, socialist idealist who fought against perceived injustice around the world, earning him a long list of enemies, particularly in South Africa, where he was a determined foe of apartheid. At the height of the Cold War, he sought a “third way” between East and West, and he opposed the war in Vietnam.

Mr. Petersson said he had reached his conclusions after an exhaustive investigation that he compared to those of the Kennedy assassination and the downing of Pan Am Flight 103 over Lockerbie, Scotland.

It was hardly a surprise, however, as the Swedish case was widely considered solved in 2018 by a freelance journalist, Thomas Pettersson, whose reporting led to Mr. Engstrom.

Mr. Pettersson, the journalist, found a link between the killer and a weapons collector, a former military man who detested Mr. Palme and his socialist ideals. Mr. Petersson, the prosecutor, said that in 2017, the police found a weapon at the collector’s house matching the one that could have been used in the prime minister’s killing. But officials could not establish definitively that the gun was the murder weapon.

The prosecutor did not name the weapons dealer, as he is not a suspect. He also said the journalist’s findings had played no role in the investigation. But he allowed that “he came up with the same ideas we have came up with.”

There has been widespread criticism about the way the Swedish judiciary and the police have handled the case over the past decades. The mystery endured through six investigations and three commissions over the years, but Mr. Engstrom eluded suspicion though he had presented himself to the police as a witness to the killing.