Some of the 800 National Guard members deployed by President Trump began arriving at Washington, D.C., on Tuesday, a day after the president used his executive powers to order federal forces to take over the city’s police department.

The move draws on powers granted under the Home Rule Act of 1973, which allows the president to assume control of the city’s police force for 48 hours during emergencies, with potential extensions of up to 30 days. But on Tuesday, Mr. Trump made clear that he will set the timetable.

“The mobilization and duration of duty shall remain in effect until I determine that conditions of law and order have been restored in the District of Columbia,” he said in a memorandum, directing the secretary of defense to “mobilize the District of Columbia National Guard and order members to active service, in such numbers as he deems necessary, to address the epidemic of crime in our Nation’s capital.”

While D.C. officials and Democrats have downplayed crime in the city, a man was shot and killed just hours after Mr. Trump announced the federal takeover of the Metropolitan Police Department. The victim was found in the 1200 block of 12th Street Northwest with multiple gunshot wounds.

In a “Memorandum for the Secretary of Defense” put out by the White House on Tuesday, Mr. Trump wrote that “the local government of the District of Columbia has lost control of public order and safety in the city, as evidenced by the two embassy staffers who were murdered in May, the Congressional intern who was fatally shot a short distance from the White House in June, and the Administration staffer who was mercilessly beaten by a violent mob days ago.”

“Citizens, tourists, and staff alike are unable to live peacefully in the Nation’s capital, which is under siege from violent crime.  It is a point of national disgrace that Washington, D.C., has a violent crime rate that is higher than some of the most dangerous places in the world.  It is my duty to our citizens and Federal workers to secure the safety and the peaceful functioning of our Nation, the Federal Government, and our city,” he wrote.

Also on Tuesday, Attorney General Pam Bondi, the FBI director, Kash Patel, Deputy Attorney General Todd Blanche, the DEA administrator, Terry Cole, and the U.S. Marshals Service director, Gady Serralta, met with D.C.’s mayor, Muriel Bowser, and the D.C. police chief, Pamela Smith, about Mr. Trump’s directive.

“I’m focused on the federal surge and how to make the most of the additional officer support that we have,” Ms. Bowser told reporters after the meeting. “We have the best in the business and Pamela Smith to lead that effort, and to make sure that the men and women who are coming from federal law enforcement are being well used.”