Taliban spokesperson Zabihullah Mujahid made the claim to local newspapers as well as on one of the militant Islamist group's websites, according to a report from Javed Hamim Kakar at the Afghan news agency Pajhwok.
Mujahid is known as an official Taliban spokesperson under the leadership of Mullah Omar, head of the Taliban in Afghanistan.
In an interview with Swedish news agency TT in the autumn, Mujahid said:
"Send your troops home. We do not want to kill Swedes and we do not want you to kill Afghans, but that will be the result of the troops' presence."
"Furthermore, the Swedish troops are not here to defend Sweden. Or to help the people of Afghanistan. You are here on the orders of the USA - you are the Americans' slaves."
Whether the claims of responsibility for the killings are true or false is impossible to establish. It is well known that the Taliban has a tendency to claim responsibility for every attack it deems successful.
28-year-old Captain Johan Palmlöv and 31-year-old Lieutenant Gunnar Andersson, and their Afghan interpreter Mohammad Shahab Ayouby, were part of a patrol which came under fire on Sunday near a police station, 40 kilometres west of Mazar-e Sharif, near the village of Gurgi Tappeh.
Soldiers in the patrol have confirmed that their attacker was dressed in an Afghan police officer's uniform. His identity is the subject of the military police investigation.