Nils Horner was shot at close range in an execution-style attack in an upmarket district of the Afghan capital, a city that is regularly hit by Taliban suicide attacks.
Yesterday's killing was claimed by Fidai Mahaz, a small splinter group linked to the Taliban-led insurgency that fights against the US-backed government in Kabul.
"Nils Horner was killed in this attack. He was not a journalist he was a (British) spy," said a statement on the group's website.
Taliban sources in neighbouring Pakistan described the group as specialising in criminal activity, targeted killings and kidnapping.
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Afghan authorities said they were aware of the Fidai Mahaz claim, but declined to comment further.
"We are making a lot of effort to catch the perpetrators," said interior ministry spokesman Sediq Sediqqi.
"Two people were possibly involved in the murder of Mr. Horner, they are the main suspects and were seen by witnesses. We are trying to get their images from CCTV."
Foreigners have been targeted before at guesthouses, luxury hotels and embassies in the heavily guarded city, but few have been gunned down in the street in daylight.
On the day of Horner's death, many of Kabul's security forces were on duty at the funeral of Vice-President Marshal Mohammad Qasim Fahim.
Horner, 51, was an experienced Hong Kong-based reporter who had previously been in Afghanistan to witness the fall of the Taliban in 2001 and in Iraq during the war in 2003.