Sweden's national police force (Rikskriminalpolisen) has opened a case into the murder of the 51-year-old Swede, whose death sent ripples around the world on Tuesday. It remains unclear whether or not the Swedish police will send officers to Afghanistan.
The Swedish Prosecution Authority (Internationella åklagarkammaren) also launched an investigation on Thursday.
Horner, a 51-year-old journalist working as Sveriges Radio's South Asia correspondent, was on his way to interview the survivor of a Taliban attack at a nearby restaurant where 21 people, including 13 foreigners, were murdered in January.
The Taliban denied any involvement in the attack. On Wednesday, an Islamist group took responsibility for the murder, claiming that Horner was a British spy.
Local police have not made any arrests.
The Swedish government plans to steer clear of the Afghan police's murder investigation.
"We are following everything that is happening but at the moment it is a matter for the police. We are not involved," foreign affairs ministry spokeswoman Lena Tranberg told AFP.
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The murder of Horner, who is a dual British and Swedish citizen, prompted concern from Tony Hall, the Director-General of the BBC.
"Journalists have become victims," he told Sveriges Radio (SR). "The immunity that they used to have when they reported for us seems to have vanished. And this is a change that has become all the more clear over the past 20 or maybe even ten years."