Six members of Congress have asked Attorney General Eric H. Holder Jr. to open a federal investigation into the circumstances surrounding the death of a Staten Island man in police custody, and to extend the inquiry into other possible civil-rights violations committed by the Police Department through its “broken windows” approach to fighting crime.

In a letter sent to Mr. Holder on Wednesday, the representatives, all New York City Democrats, urged the Justice Department to intervene in the case immediately, and not wait for Daniel M. Donovan Jr., the Staten Island district attorney, to complete his own inquiry into the death of the man, Eric Garner.

The fatal encounter between Mr. Garner and plainclothes police officers from the local precinct on the north side of Staten Island began when the officers accused Mr. Garner of peddling untaxed cigarettes and sought to arrest him. The officers restrained Mr. Garner in the struggle that ensued, and he died soon after. The city medical examiner’s office ruled that Mr. Garner’s death was a homicide and that it was caused by compression of his chest and a chokehold applied as he was being subdued.

Mr. Garner’s death has ignited outrage and protests over the excessive use of force by the police, and has spurred a larger debate over the Police Department’s adherence to the broken-windows strategy, which holds that enforcing low-level offenses helps prevent more serious crimes.

“Mr. Garner’s death has taken place in the context of a broken windows policing strategy that appears to target communities of color for the enforcement of minor violations and low-level criminal offenses,” the letter says.

“To the extent the N.Y.P.D. is engaging in a racially selective law enforcement campaign pursuant to its broken windows approach, the constitutional and federal civil rights of black and Latino residents may be in jeopardy,” the letter continues.

The letter is signed by Representatives Yvette D. Clarke, Hakeem Jeffries, Gregory W. Meeks, Charles B. Rangel, Jose E. Serrano and Nydia M. Velázquez, who also express a lack of confidence in the way Mr. Donovan, a Republican, is handling the case.

“There is no indication that the local district attorney is prepared to aggressively prosecute this case,” the letter says. “Absent D.O.J. intervention, we may be marching toward a miscarriage of justice,” it adds, in a reference to the Justice Department.

The letter does not specify why the officials doubt the integrity of Mr. Donovan’s investigation, beyond noting that the officer who had his arm around Mr. Garner’s neck, Daniel Pantaleo, remains free. “The lack of action is deeply troubling,” the letter says.

A spokesman for Mr. Donovan, Douglas C. Auer, would say only that the district attorney’s office was “continuing with its investigation into the circumstances surrounding Mr. Garner’s death.”

Officer Pantaleo’s union representatives have said that the officer’s maneuver did not amount to a chokehold and that any legal defense would rely on police experts in the use of force.

A spokeswoman for the Justice Department said the letter was being reviewed. Mr. Holder himself has said previously that the department is closely monitoring the matter. A Police Department spokesman did not immediately return a call seeking comment.

Asked in an interview why he felt the Justice Department should act before the district attorney’s office has concluded its inquiry, Mr. Jeffries said that Mr. Donovan, as the local prosecutor, “institutionally has a close relationship with the Police Department, as he should, but in instances where a police officer has been implicated in a potentially serious violation of the law, it’s appropriate for another level of government to step in and impartially investigate the matter.”

Mr. Jeffries also noted that the man who videotaped the encounter between Mr. Garner and the police has since been arrested on gun possession charges, which, he said, heightened the need for an outside prosecutor.

“Eric Garner is dead,” Mr. Jeffries said. “The person who videotaped the incident was arrested. And the officer who killed Mr. Garner in broad daylight remains free and on the N.Y.P.D.’s payroll. There’s something wrong with that picture.”