He apologized for the leak, which he said involved combinations of names, identification numbers, birth dates and addresses.
The pension service was setting up a team to investigate the cause and prevent a recurrence, Mizushima said.
"These are the people's vital pensions. I have instructed Health and Welfare Minister (Yasuhisa) Shiozaki to consider the pension recipients and do everything possible," Abe told reporters in brief remarks aired on NHK public television, which featured the data leak as the evening's top news story.
Separately, Shiozaki apologised for failing to prevent the hacking and told a news conference he had instructed the Japan Pension Service to set top priority on protecting the public's pensions.
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Public outrage over botched record-keeping that left millions of pension premium payments unaccounted for was a major factor in a devastating defeat suffered by Abe's Liberal Democratic Party in a 2007 election for parliament's upper house.
Abe, whose first cabinet also lost several cabinet ministers to other scandals and gaffes, including one who committed suicide, resigned in September of that year in the face of parliamentary deadlock and ill health.