Noncitizens are counted when determining how to apportion the 435 House seats among states. But in his new memo Mr. Trump said it is the policy of the U.S. to exclude unauthorized immigrants from the apportionment process.

Democratic lawmakers and outside groups quickly criticized the move as violating the Constitution.

“This is blatantly unconstitutional. The Constitution’s text is clear,” said Elizabeth Wydra, the president of the liberal Constitutional Accountability Center. “The federal government has a constitutional obligation to count all people living in the United States, whether they are citizens or noncitizens, whether they were born in the United States or in a distant part of the world.”

The American Civil Liberties Union, which led a successful legal challenge against Mr. Trump’s earlier attempt to add a citizenship question to the census, said it would fight the president’s move in court.

The Constitution mandates that the government conduct an “enumeration” of the population every 10 years for the purpose of apportioning congressional representatives. The 14th Amendment says the representatives should be apportioned by counting the “whole number of persons in each state.”

The House Oversight Committee said it would hold an emergency hearing on the census next week.

“By excluding undocumented immigrants from apportionment or redistricting, this administration departs from more than two centuries of practice and constitutional understanding,” Committee Chairwoman Carolyn Maloney (D., N.Y.) said Tuesday.

The Census Bureau said earlier this month that it would begin deploying hundreds of thousands of enumerators to knock on millions of doors nationwide, after the agency delayed parts of the 2020 count because of the coronavirus pandemic. So far, 91 million households, or 62% of those in the U.S., have responded to the census since the bulk of the decennial population tally got under way in March.

The Trump administration last July abandoned its bid to include a question on the census asking people about their citizenship status, amid a series of legal challenges including a Supreme Court ruling halting the effort. Democrats and activists warned the effort would discourage many immigrants, including those who aren’t in the country legally, from participating. Instead, Mr. Trump signed an executive order at the time requiring federal agencies to share information with the Census Bureau to assist in collecting U.S. residents’ citizenship details.

But obtaining an accurate count of unauthorized residents from that data would be extremely challenging. The order would let the agency match census responses with citizenship-verified records such as Social Security and passport records to produce local counts of citizens and noncitizens. However, such records typically verify only whether someone is a citizen or legal immigrant. Subtracting both groups from total population counts would let the Census Bureau indirectly produce estimates of unauthorized immigrants.

Federal law prohibits the bureau from using census data “for any purpose other than the statistical purposes for which it is supplied,” and from releasing statistics in a form that would allow an individual to be identified.

Lawmakers of both parties have called on the Trump administration to ensure the census is conducted accurately.

“It is imperative for the Census to count every person in the United States, where they live, and this includes communities that for various reasons have historically had low participation in decennial censuses,” Sen. Jerry Moran (R., Kans.) and Jeanne Shaheen (D., N.H.) wrote in a letter to Census Director Steven Dillingham earlier this month, adding that they would be watching closely to ensure data processing is “free from political interference.”