TOKYO—Prime Minister Shinzo Abe’s government is easing the path for foreign workers, with new policies that include a pledge to deliver the world’s fastest permanent-residency cards for skilled migrants.

A set of immigration measures, including that one, was buried amid dozens of ideas released last week in Mr. Abe’s annual list of policy changes. The government also said it planned to bring in more workers for understaffed nursing homes and 2020 Tokyo Olympics construction projects.

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