President Trump on Monday signed an order creating a federal task force and authorizing the use of the National Guard to crack down on crime in Memphis over the concerns of local Democratic lawmakers who are wary of a surge of policing from Washington.

Speaking from the Oval Office alongside Gov. Bill Lee of Tennessee and the state’s two Republican senators, Marsha Blackburn and Bill Hagerty, all Republicans, Mr. Trump said the task force would be a “replica” of the large show of police and military forces currently on display in Washington.

Mr. Trump said he would also consider sending federal law enforcement officials into Chicago, St. Louis and New Orleans.

“We’re going to take care of all of them step by step, just like we did in D.C.,” Mr. Trump said.

Details were scarce on Mr. Trump’s plans for Memphis, which he announced days earlier in an interview on Fox News, but the president said multiple federal agencies would be involved. In addition to working with state and local law enforcement in Tennessee, as well as Mississippi and Arkansas, it allows for the mobilization of National Guard units at Mr. Lee’s request.

Mr. Lee requested the federal assistance, Mr. Trump said. Crime rates in Memphis have dropped this year compared with recent years, according to local police, though they still remain high compared to other parts of the country.

“I’m tired of crime holding the great city of Memphis back,” said Mr. Lee, who is in his final term as governor. Earlier this year, he dispatched members of the Tennessee National Guard to Washington to help with Mr. Trump’s efforts there.