In announcing the execution of the final six members, who were all on death row, Justice Minister Yoko Kamikawa repeatedly said the executions were carried out after careful deliberation and in consideration of the fear, pain and sadness inflicted on numerous victims of the cult's crimes.
There are four remaining members on death row.
The group was responsible for the 1995 sarin gas attack in the Tokyo subway system that killed 13 people and injured more than 5,500.
Under instructions from Asahara, several AUM members released sarin gas from a vehicle mounted with a spraying device at a parking lot in a residential district of the city of Matsumoto, Nagano Prefecture, central Japan, on the night of June 27, 1994.
The other member put to death is still unclear. The group released sarin from a truck while driving around an apartment complex, CNN reported. Authorities raided its headquarters near Mount Fuji in 1995, and captured Asahara about two months later.
Its name, Aum Shinrikyo, means Supreme Truth.
"With the 13 members executed, perhaps the case is closed from the point of view of criminal justice", Shizue Takahashi, whose husband was killed in the subway attack, told reporters.
Aum Shinrikyo gained official status as a religious organisation in Japan in 1989 and picked up a sizeable global following.
Japan has executed the final six members of a doomsday cult behind the worst terrorist attack in its history.
Aum members have also been convicted of an additional sarin attack in the town of Matsumoto the year before the Tokyo attack, as well as the murder of an anti-cult lawyer and his family.
It is still legal in Japan, although designated as "dangerous religion" subject to surveillance. There are now 110 people on death row in Japan, with 88 of those appealing their cases, CNN reported.