The rule—which injects a new civil-rights issue into the debate about U.S. immigration-policy changes—would require collection of cheek swabs from what could amount to hundreds of thousands of migrants, including unauthorized immigrants taken into Immigration and Customs Enforcement custody.

The move would be a significant expansion of the government’s DNA database, operated by the Federal Bureau of Investigation, that contains samples from people accused of committing serious crimes.

Senior Justice Department officials said the expansion brings the government in better compliance with a 2005 law directing it to collect biometric information from several groups of people, including criminals and unauthorized immigrants, though that law gave the Homeland Security secretary discretion to waive the requirement. The Justice Department officials also said the Trump administration feels compelled to move ahead with the plan because it would help the government better identify immigrants who could commit crimes in the future.

The government’s decision alarmed immigrant- and civil-rights advocates, who said collecting DNA samples from people who haven’t committed crimes—many immigrants enter the country at legal ports of entry to ask for asylum—would amount to significant violations of privacy.

The practice also could result in discriminatory profiling by other law-enforcement agencies that might have access to the DNA of the immigrants, they said.

“Forced DNA collection raises serious privacy and civil liberties concerns and lacks justification, especially when DHS is already using less intrusive identification methods like fingerprinting,” said Vera Eidelman, staff attorney with the American Civil Liberties Union’s Speech, Privacy, and Technology Project.

“Moreover, it is worth considering the full intersection of the government’s asserted powers when we think about the consequences of it collecting such deeply sensitive, personal, identifying information about us and on such a massive scale,” Ms. Eidelman added.

The move is part of the Trump administration’s broader shift to consider most immigrants entering the country, even those who come to legal ports of entry, as criminals. It has made all unauthorized immigrants targets for deportation, a departure from the Obama administration’s policy. Crossing the border illegally a first time is currently considered a misdemeanor under federal law.

DHS officials said Wednesday they were required to take the step under the DNA Fingerprint Act of 2005, part of President George W. Bush administration’s response to the Sept. 11 terrorist attacks.

The government hasn’t collected DNA from immigrants under an agreement between then-Attorney General Eric Holder and Homeland Security Secretary Janet Napolitano during President Obama’s first term.

DHS officials said Wednesday that they are setting up a task force ahead of the new Justice Department rule to sort out the operational difficulties of collecting DNA samples from potentially hundreds of thousands of immigrants each year. They said immigration officials charged with collecting DNA would be trained to safeguard immigrants’ privacy.

ICE officials began a pilot program this summer using DNA sampling on immigrant families, to ensure the adults were related to the children traveling with them. The Trump administration has long suspected that adult migrants bring unrelated children with them to be treated as families by the U.S. immigration system—meaning they couldn’t be kept in government custody longer than 20 days.

That pilot program, which required less intensive DNA sampling, inspired the larger effort, the officials said.

The new program will require immigration agents to collect a more comprehensive DNA sample, so that the DNA can later be used to help identify criminal suspects.

Write to Michelle Hackman at Michelle.Hackman@wsj.com