His youngest daughter, whose name has not been made public, is the only one of Asahara's children to break with the successor group.
"I was very surprised, but I have decided to accept his will as my father's last message," she said in a statement posted on her lawyer's blog.
She urged her relatives and his followers to accept the decision and called on cult members to "put an end to the Aum and stop hating society".
The announcement comes a day after Japanese authorities cremated 63-year-old Asahara, amid fears that his death could be used to reboot the cult.
Jiji news agency said Asahara's remains would stay at the detention centre where he was executed for now because of fears that his daughter could be assaulted by his followers if she came to collect them.
The near-blind leader, whose real name was Chizuru Matsumoto, was executed Friday for his role in the 1995 sarin attack on the Tokyo subway and other crimes. The subway attack killed 13 people and injured thousands. Six other members of the cult remain on death row.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)