BRUSSELS — Swedish investigators on Wednesday identified the man they think assassinated Prime Minister Olof Palme in 1986, but with only circumstantial evidence and the suspect long dead, it was a somewhat unsatisfying conclusion to one of the biggest political murder mysteries in generations.

The question of who shot Palme in the back as he walked home from the movies with his wife on a frigid Stockholm evening has stumped police and occupied Swedish imaginations ever since February 1986. Speculation about who was behind the crime included the apartheid-era South African government, which resented Palme for his outspoken left-wing views, and the Kurdish militant group the PKK. A Swedish man was sentenced to life for the crime in 1988, but his conviction was thrown out the following year on appeal.

On Wednesday, Swedish prosecutors identified a different key suspect: Stig Engstrom, then 52, a Swedish graphic designer who was vocally opposed to Palme’s left-wing policies and worked at the insurance company outside of which Palme was shot.

Chief prosecutor Krister Petersson said investigators did not conclusively link a weapon to the assassination, but with the evidence they have assembled, there would be enough to move forward with a case against Engstrom — if he were alive.

Engstrom died in 2000 in what is believed to have been a suicide.

“We’ve come as far as we are able to come when it comes to a suspect,” Petersson said during a two-hour news conference in which he and a police investigator laid out the evidence against Engstrom. “I understand that different conspiracy theories will keep afloat in the public domain, as they have in the past 34 years, but we have had our conclusion.”

Police compared their effort to the investigation of the assassination of President John F. Kennedy in 1963 and the search for the culprit in the 1988 downing of Pan Am Flight 103 over Lockerbie, Scotland.

The uncertainty surrounding the Palme assassination captivated the country’s consciousness. Swedes who were alive at the time remember where they were when they heard the news. It has been an obsession for amateur detectives and has inspired books, movies and plays — and some say Sweden’s broader success in crime fiction.

Palme was shot with a single bullet that severed his spinal cord. His wife, Lisbeth, was grazed by a second bullet but survived. They had released their security detail for the day.

Petersson said records from the Skandia insurance company showed that Engstrom walked out the front door at 11:19 p.m. on the evening of Feb. 28, 1986, two minutes before Palme was killed at the corner of the building.

Engstrom had been a sergeant in the military and remained active in a military shooting club, giving him the experience to carry out a killing. Police also learned that he had known a weapons collector who, like him, hated Palme and his policies. In 2017, the prosecutor said, police found a weapon in the collection that could have been used in the assassination, but they were unable to connect it conclusively to the killing.

Engstrom was repeatedly interviewed as a witness in the year after the assassination. Multiple other witnesses said a man who ran away from the scene was wearing clothing and other items that looked a lot like Engstrom’s that evening: a dark knitted cap, glasses, a three-quarter length coat and business shoes unsuited for the slippery Stockholm pavement. Engstrom gave a different account and said the perpetrator had been wearing a blue coat.

Police dismissed him as a suspect — a decision Petersson, who took over the case in 2017, said was inexplicable.

In the aftermath of the assassination, Engstrom was brazen in his alleged duplicity, narrating his account of his movements that night for Swedish television journalists and even wearing the clothing he was alleged to have worn during the killing — all while complaining that the police were uninterested in his testimony.

“You try to put the pieces into a jigsaw puzzle, you shouldn’t take away pieces from the jigsaw puzzle, but perhaps they’re not so good at putting the jigsaw pieces together, the police,” Engstrom said in a 1986 Swedish television clip that the prosecutor played on Wednesday.

In the clip, Engstrom reenacts exiting the blocky Skandia tower where he worked, walking around the streets of Stockholm and even running down the street in what he claimed had been a frantic attempt to catch the last train home from the Stockholm central subway station.

“My interpretation of this interview is that he’s mocking the police,” Petersson said.

The prosecutors’ conclusions announced Wednesday match those of Thomas Pettersson, a freelance journalist who published much of the same information in 2018 after a 12-year investigation. Pettersson handed over his leads to the police.

“Even if we were to continue to investigate this case for years, we would continue to see that Stig Engstrom is a suspect in this case,” said Petersson, the prosecutor. “It is difficult to see how after 34 years we could get further.”