WASHINGTON—President Trump signed a memo Tuesday meant to exclude immigrants who are in the U.S. illegally from being taken into account when the government divides up congressional seats, a move that civil-rights groups swiftly vowed to challenge in court.

The census, which the Constitution requires to be conducted nationwide every 10 years, counts every person living in the U.S., whether they are a citizen or not. Census data determines how federal resources are distributed to states and localities, as well as how congressional…

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