“It's still an open wound,” current Prime Minister Stefan Löfven told reporters after paying tribute to his Social Democratic predecessor, laying a wreath of red roses in a solemn ceremony at a Stockholm cemetery just a stone's throw from the murder scene.
Palme was killed on February 28, 1986, after leaving a Stockholm cinema with his wife Lisbet to walk home alone, having dismissed his bodyguards for the evening.
An unidentified attacker approached the couple and shot Palme in the back, leaving the 59-year-old dying in a pool of blood on the sidewalk.
The gunman ran off, taking with him the murder weapon, a .357 Magnum revolver which has never been recovered.
The murder of their charismatic leader sent Swedes into shock, and their tranquil and open society is said to have “lost its innocence” that day.
The case has never been solved, and the investigation continues: more than 10,000 people have been questioned, 134 people have claimed responsibility, and the case files take up 250 meters of shelf space.
A father and son pay their respects at the spot where Palme was murdered in 1986. Photo: Jonas Ekströmer / TT
Christer Pettersson, a petty criminal and drug addict, was convicted of the crime in July 1989 after Lisbet identified him in a widely-criticised line-up.
But he was freed months later by an appeals court which dismissed Lisbet's testimony on a technicality. He died in 2004.
Police were heavily criticised for botching the early stages of the investigation, failing to cordon off the scene properly and allowing onlookers to walk around and destroy potential forensic evidence.
Over the years, investigators have suspected Turkey's Kurdish rebel group the Kurdistan Workers' Party (PKK), the Swedish military and police, and the South African secret service among others.
Chief investigator Kerstin Skarp said nonetheless last week she remained “optimistic” the case would be solved one day.
Löfven said on Sunday he thought the murderer had already been caught.
The Swedish prime minister, Stefan Löfven at the ceremony to commemorate Palme's life. Jonas Ekströmer / TT
“We have a witness, Lisbet Palme, who said it was Christer Pettersson, and I believe that.”
A left-wing activist in his youth, Palme was a controversial figure at home.
He was known as a great orator, but was disliked by some for his perceived arrogance, especially among conservatives who saw the wealthy-born Palme as a class traitor.
He infuriated Washington with his vocal opposition to the US war in Vietnam. He backed leftist governments in Cuba and Nicaragua, and spoke out against apartheid and nuclear power.
At home, he laid the foundation for Sweden's modern-day gender equality, encouraging women into the workforce by overseeing the abolition of joint spousal tax declarations, the introduction of parental leave pay and universal daycare, and the right to free abortion.