Mayumi Moriyama told a cabinet meeting that "there is still the danger that the group may engage in acts of indiscriminate mass murder" and called for "continued vigilance" of Aum Shinrikyo.
Ms Moriyama was speaking after the release of an annual report on the group, as part of legislation aimed at monitoring the cult.
Several members of Aum Shinrikyo have so far been sentenced for their roles in the cult's crimes. The founder of the group, Shoko Asahara, is still on trial.
Aum Shinrikyo
The latest report on the group, compiled by the Justice Ministry's Public Security Investigation Agency, said that Aum had about 650 live-in followers and some 1,000 outside believers, as of the end of last December.
Aum went bankrupt in 1996, after the arrest of its top leaders. It has since changed its name to Aleph and claims to have renounced violence under its new leader, Fumihiro Joyu.
But Ms Morayama told a news conference that under Mr Joyu's leadership, the group continues to worship Asahara's "dangerous" teachings.
The group maintains 28 offices and 120 apartments in 17 prefectures throughout Japan and has 300 members in Russia, the report on Aum said.
The cult uses different names to offer yoga lessons and computer classes in order to finance its activities and recruit new members, the report added.
On Thursday, the Tokyo District Court held the last questioning session for Asahara, as his trial, in its seventh year, neared its final stage.
Asahara, whose real name is Chizuo Matsumoto, was reported to have remained silent during the hearing. Prosecutors are scheduled to close their case 24 April, and are expected to seek the death penalty.
The 1995 sarin gas attack killed 12 people and left thousands ill.
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