Kamikawa told a news conference that she had ordered the executions following "very careful consideration".
Tomomasa Nakagawa, a doctor also executed Friday, and several other cultists broke into the Sakamotos' apartment late at night, strangled them to death and buried them in the mountains.
Japan, which generally reserves capital punishment for people convicted of multiple homicides, usually executes a handful of people each year.
In the following months, members of the cult carried out several failed attempts at releasing hydrogen cyanide in various stations.
While the execution of Aum Shinrikyo cult founder Shoko Asahara and six of the group's former senior members may have drawn the curtain on a string of crimes that shocked Japan, it opens the door for society to engage in further debate about the death penalty. Asahara and six followers were executed Friday for their roles in a deadly 1995 gas attack on the Tokyo subways and other crimes, Japan's Justice Ministry said.
The leader of cult movement Aum Shinrikyo, Shoko Asahara, and six of his followers were executed on Friday.
Atsushi Sakahara, who was injured in the attack, welcomed the executions.
Aum Shinrikyo attracted young, well-educated adherents, including scientists who then helped produce the poisons used in the cult's attacks. Some said Japan has now lost a chance to hear an account of the crimes from Matsumoto, who had stopped making meaningful speeches from the middle of his first trial, which started in April 1996.
Shizue Takahashi, whose subway worker husband was killed in the attack, told reporters she felt Asahara's execution was entirely appropriate.
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"A third of my life has been affected by AUM".
"With the execution, I feel that the opportunity to discover (why) has been lost", Moriyama said.
Chizuo Matsumoto, the cult's leader who went by the name Shoko Asahara, was the first to be hanged, media said as it broke into regular programming to report the news. Executions are carried out suddenly with little warning to the condemned or their families when the day arrives, following a conviction and appeals process that can stretch out for years, as it did with Asahara. On February 27, 2004, he was sentenced to death by hanging. Asahara was arrested in May 1995. About 180 members were sentenced to varying prison terms.
Japan forgoes executing death row inmates if an accomplice is still on trial.
AUM evolved from a yoga school established by Asahara in 1984 and had about 1,400 live-in followers and over 10,000 lay followers at one point.
Rights group Amnesty International said justice demanded accountability but also respect for civil rights. Over the years, the group managed to lure in followers from some of Japan's top universities and boasted some 10,000 followers in Japan and another 30,000 in Russian Federation.
His followers claimed their guru, who dressed in Chinese-style pyjama tunics, had extra-sensory powers and could levitate for hours at a time.
The ensuing raid on the cult's compound near Mount Fuji riveted Japan, as 2,000 police officers approached with a canary in a bird cage.