Of particular concern for some officials is the prospect that Mr. Trump may be planning to announce a pardon for Joe Arpaio, the former sheriff of Maricopa County, Ariz., who became an avatar for hard-line policies with his roundups of undocumented immigrants. Some of Mr. Trump’s advisers worry that a pardon could deepen the racial wounds exposed in the last week and compound the president’s political problems.

A person close to Mr. Trump said the president had discussed a pardon for Mr. Arpaio, who was found guilty of criminal contempt of court when he defied a judge’s order in a case involving racial profiling. Mr. Arpaio was accused of disregarding a 2011 order from a federal district judge prohibiting deputies from detaining people simply because of immigration offenses.