A spokesman for Kabul's criminal investigation section told The Canadian Press that Nils Horner, 51, was shot in the back of the head while talking to a translator on a street that runs along the Afghan capital's embassy district. The scene lies just up the way from the site of a deadly restaurant attack in January.
Horner, who was also a British citizen, was rushed from the scene, but succumbed before reaching the hospital, said Sayed Gul Agha Hashimi.
The journalist's driver and translator are being questioned as part of the investigation.
A witness, who didn't want to give his name, said two young men approached Horner just after he'd gotten out of a car and while he was in conversation with the translator.
He said the men's appearance didn't raise any alarm and it seemed they all knew each other. Then one of the men pulled out a gun with a silencer and shot Horner.
British news media reports say Horner had been on his way to meet a survivor of the January restaurant attack, in which Taliban militants killed 13 foreigners and eight Afghans.
Police say they are investigating whether the shooting was motivated by a personal issue or was an insurgent strike.
"The police do not have any evidence to say who was behind this attack, but after the investigation we will know whether this incident was political or personal," police spokesman Hashmat Stanikzai said.
Taliban spokesman Zabihullah Mujahid told The Associated Press that his group was not responsible.
The area where Horner was killed teems with private security and Afghan police. There are multiple road barriers, blast walls and sand-bagged machine gun posts.
Late Tuesday, an official with the Swedish embassy was at the guest house where Horner lived and where his room has been sealed off. Police are expected to search it on Wednesday.
Anne Lagercrantz, head of news at Swedish Radio, said the newsroom was in deep shock.
She said Horner spoke to the desk in Stockholm early Tuesday and they agreed that he would go out and do interviews ahead of the election.
When people in the newsroom saw reports that a foreign journalist had been shot in Kabul, they tried to contact Horner by email but got no response. They then called his mobile phone, and a doctor answered saying Horner had been shot and killed, Lagercrantz said.
Horner had worked for Swedish Radio SR since 2001 as a foreign correspondent mostly in Asia and the Middle East, including Afghanistan and Baghdad.
Swedish Radio chief executive Cilla Benko said Horner was very safety conscious but was prepared to take risks.
"This was his life," Benko said. "He didn't want to do anything else."
Suicide bombings and other attacks are regular events in Kabul, especially in the run-up to the April 5 election, but the targeted killing of journalists and other foreigners is extremely rare.
Criminal gangs and sometimes insurgents prefer kidnapping to murder.
The scene was still cordoned off Tuesday afternoon and the attack happened as the city was in high-security mode for the funeral of Afghanistan's powerful Vice-President Mohammed Qasim Fahim.
Traffic was snarled throughout the city, with thousands lining the streets to pay their respects as Fahim's flag-covered coffin was carried to the grave by ambulance.
Fahim, who died on Sunday at 57, was an ethnic Tajik and a leading commander in the Northern Alliance, which fought the Taliban for years and helped the U.S. oust the Islamic militant movement.
His death came a month before elections to choose a successor to President Hamid Karzai, who is barred from seeking a third term.
- with files from The Associated Press