"We killed Sushmita Banerjee because she is an Indian spy," the group's spokesman Qari Hamza told The Daily Beast, the online home of Newsweek magazine.
He admitted that his men kidnapped, harshly interrogated, and then killed her.
"We took her from her house, investigated her for three hours and then left her dead," he said.
Banerjee, 49, was married to Afghan businessman Jaanbaz Khan and recently moved back to Afghanistan to live with him.
She was killed by militants in eastern Paktika province of Afghanistan last week.
According to the news portal, Hamza claimed that during their "investigation Sushmita Banerjee also disclosed the names of other agents and we will go after them as well".
The writer's relatives and friends in Kolkata have alleged there was a conspiracy by her husband and demanded a proper probe into her death.
Banerjee's book Kabuliwalar Bangali Bou (A Kabuliwala's Bengali Wife), about her escape from the Taliban in 1995, became a bestseller in India and was made into the Bollywood film Escape From Taliban in 2003.
The memoir focused on her life in Afghanistan with her husband and her escape from the militants.
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Indian author Sushmita Banerjee shot dead in Afghanistan