Such reactions to Mr. Trump’s pardon reflect the enduring outrage over Mr. Arpaio’s actions as the longtime sheriff of Maricopa County, which encompasses Phoenix. Before his ouster by voters in November, Mr. Arpaio gained notoriety as an immigration hard-liner and one of Mr. Trump’s most prominent supporters in the Southwest.

But Mr. Arpaio, 85, was also found guilty of criminal contempt just weeks ago in connection to a case that has caused tempers to flare in Arizona, and around the country, for the past decade. Plaintiffs claimed that Mr. Arpaio regularly violated the rights of Latinos by racially profiling and detaining them.

Judge Susan R. Bolton of United States District Court ruled that Mr. Arpaio had willfully violated a court order in 2011 to halt his practices. The ruling was hailed by many liberal and conservative Latinos alike as proof that justice could be served even on such a powerful figure as Mr. Arpaio, who could have faced up to six months in jail.

With the pardon, however, Mr. Trump is handing some of his most ardent critics a way to attack the president.

“Donald Trump is an absolute coward for pardoning a man who engaged in racist police practices,” said Representative Ruben Gallego, Democrat of Arizona. “Arpaio was finally found guilty, but this shows that the legal system cannot deliver justice. We’ll now seek justice through elections, and Republicans in open districts of Arizona should be on edge.”