The unsolved murder of Swedish Prime Minister Olof Palme, who was shot dead 34 years ago in Stockholm, may be a step closer being solved.

The case's chief prosecutor, Krister Petersson, says he is "positive about being able to present what happened and who is responsible for it.”

"My goal is to present (a charge in the case) in the first half of 2020," Petersson told Swedish broadcaster SVT, Tuesday. "I am optimistic. We have worked hard, and we have leads in which we believe a lot.”

Asked whether the investigation had gotten closer to solving the case, Petersson replied "in my opinion, yes."

Petersson, who didn't name any suspect or give any date for announcing a charge, said the case otherwise would be closed.

Palme was gunned down Feb. 28, 1986, after he and his wife Lisbeth left a movie theater in Stockholm. Palme, who attempted to live a normal life despite his high profile, had dismissed his bodyguards for the night. 

Following his death, thousands of shocked Swedes flooded the murder scene with red roses, a symbol of Palme's Social Democratic Party. 

Lisbeth, who was injured in the attack, later identified the shooter as Christer Pettersson, who was convicted of Palme's murder in 1988. 

Christer Pettersson, no relation to the chief prosecutor, later had his sentence overturned, in 1989, due to a lack of evidence, including the missing murder weapon.

Investigators have interviewed over 10,000 people while more than 130 have claimed responsibility for the assassination. The murder has remained an unsolved mystery, leading to a multitude of journalists' investigations and conspiracy theories.

In Sweden Palme introduced many of the policies that are today synonymous with the country's welfare state, overseeing the introduction of paid parental leave, universal daycare, and the right to free abortion. 

Internationally, Palme backed a non-alignment policy, distancing Sweden from both the USA and Soviet Union and backing anti-colonial movements and revolutionary governments across the world.