"Please try it hard," Toranosuke Katayama said in a talk show on the private Asahi network when asked about plans by one local authority to attempt to penetrate the system.
The remark came a day before the nationwide computerised system, criticised for ushering a high surveillance Big Brother society in Japan, was due to expand its service.
The government is assigning each of Japan's 126 million citizens an 11-digit ID number in the new basic resident registry network. It contains names, birth dates, gender and addresses and enables local authorities to identify people online across the country.
The idea is to streamline Japan's cumbersome bureaucracy by making it easy to obtain basic personal information during administrative procedures.
Since the computerised ID system switched on in early August, Japanese citizens have dropped out in droves from what many resent as intrusive monitoring of the people. Critics worry about loss of privacy, the network’s security from hackers, and some fear government officials will misuse the information.
"Giving a number to people is a violation of our individual human rights"
The dozens of protest groups that have popped up have held rallies at which demonstrators showed their outrage by ripping up the papers being sent out by the government to assign every citizen their number.
"To start with, giving a number to people is a violation of our individual human rights," Eiji Yoshimura, one of the protesters, told the Associated Press. "We have absolutely nothing to gain from this system."
Several local governments have refused to participate in the system, which began last Monday. Yokohama, a Tokyo suburb of 3.4 million people, is giving its residents a choice of hooking up or not.
The disenchantment some Japanese have expressed towards the registry underlines a deep, although often hidden, distrust of government that is surprisingly common in a nation known for orderly, conformist behaviour.
"I don't especially enjoy being called by a number. It feels like (being) a prisoner," said Yasuyoshi Ban, a 60-year-old truck driver.
The home minister’s invitation to hackers to try and penetrate the system betrays what many Japanese see as a complacent government attitude towards computer-based crime.
Reminiscent of George Bush’s “Bring them on” taunt to resistance fighters in Iraq, Katayama’s comments come during a week when the internet virus Sobig.F has wrought havoc on computer networks worldwide, particularly in East Asia.
Japan’s economy, trade and industry ministry was forced to scrap a national hacking competition scheduled for this month, that was intended to foster computer expertise among high school students.
The planned event prompted a flood of angry phone calls and mail, accusing the government of encouraging cyber crime.