The attack on Yousufzai, who had been advocating education for girls, drew widespread condemnation.
Interview with Yousufzai and father
Pakistani surgeons removed a bullet from near her spinal cord during a three-hour operation the day after the attack last week, but she now needs intensive specialist follow-up care.
Authorities have said they have made several arrests in connection with the case but have given no details.
described Yousufzai as a "spy of the West".
"For this espionage, infidels gave her awards and rewards. And Islam orders killing of those who are spying for enemies," the group said in a statement.
"She used to propagate against mujahideen (holy warriors) to defame (the) Taliban. The Quran says that people propagating against Islam and Islamic forces would be killed.
"We targeted her because she would speak against the Taliban while sitting with shameless strangers and idealized the biggest enemy of Islam, Barack Obama."
Symbol of resistance. Lahore protest (Photo: AFP)
Yousufzai, a cheerful schoolgirl who had wanted to become a doctor before agreeing to her father's wishes that she strive to be a politician, has become a potent symbol of resistance against the Taliban's efforts to deprive girls of an education.
Pakistanis have held some protests and candlelight vigils but most government officials have refrained from publicly criticizing the Taliban by name over the attack, in what critics say is a lack of resolve against extremism.
"We did not attack her for raising voice for education. We targeted her for opposing mujahideen and their war," said the Taliban. "Shariah (Islamic law) says that even a child can be killed if he is propagating against Islam."
Meanwhile, British police have questioned two people at a hospital where the teenager is recovering, raising fears about her safety amid pledges by the Taliban to finish the job.
Interior Minister Malik prays for Yousufzai (Photo: AP)
Medical Director Dave Rosser of the Queen Elizabeth Hospital in Birmingham stressed Tuesday that security was "under control" at the hospital after the overnight incident. He said several people had turned up at the hospital claiming to be the girl's relatives but didn't get very far.
He said the people were arrested, but police said they had only been questioned.
"We don't believe there's any threat to her personal security," Rosser told journalists, explaining the hospital did not believe the suspects were related to Yousufzai. "We think it's probably people being over-curious."
Police would not immediately confirm the details of the incident.
Also Tuesday, Pakistani Interior Minister Rehman Malik announced a $1 million bounty for Pakistani Taliban spokesman Ahsanullah Ahsan, saying he was the one who announced that the Taliban carried out the attack on Yousufzai.