The police officers involved in the fatal shooting of a 22-year-old black man in Utah, whose family's lawyers say was shot while running away, have been identified as corporal Matthew Schauerhamer and officer Nicholas Judson.

Two sources familiar with the investigation into Darrien Hunt's death confirmed the involvement of Schauerhamer to the Guardian on Friday. A press release from Saratoga Springs police department later confirmed that Judson was the second officer involved.

In a statement, the department said it wished to "express our sympathies to all parties involved in the officer involved shooting of Darrien Hunt". It added: "Our condolences go out to Mr Hunt's family during this difficult time as they have lost a family member."

The police department said that it had "confidence in its officers and the training they receive". Schauerhamer and Judson have both been placed on paid leave while the shooting is investigated. Both are now due to have been interviewed.

The names of the officers were disclosed after Hunt's family asked the Obama administration on Friday to open a federal inquiry into his killing and the conduct of the city's police department.

Hunt died after being shot repeatedly following a confrontation with two officers outside a drive-through bank in a strip mall in Saratoga Springs early on 10 September.

Police and prosecutors say that Hunt lunged at the officers with a decorative samurai-style sword as they responded to an emergency call reporting that he was acting suspiciously. Attorneys for his family say that a private autopsy has concluded that he was then shot six times from behind while running away.

An inquiry into the incident is being carried out by a team of officials from various agencies in Utah county that is convened to look into shootings by police. Its findings are expected to be collected and published in a report by the office of the county attorney.

But Randall Edwards, the lead attorney for the Hunt family, said that he would use a press conference in Salt Lake City on Friday afternoon to announce their call for a federal investigation into a potential breach of their son's civil rights.

"We want the justice department to find out whether there was wrongdoing in the death of Darrien Hunt," Edwards told the Guardian beforehand. "We believe that the county investigation does not go to the civil rights aspect of this. And if you shoot someone down in cold blood, then obviously you're depriving them of their civil rights."

Their request follows the justice department's decision to open a civil rights inquiry into the fatal police shooting last month of Michael Brown in Ferguson, Missouri. Officer Darren Wilson's killing of Brown, an unarmed black 18-year-old, led to nights of intense clashes between young protesters and police on the streets of the St Louis suburb.

Edwards said that Hunt's family also wanted "to find out if there is a pattern, custom, policy or practice of police abuse and deprivation of civil rights" in Saratoga Springs, which is about 35 miles south of Salt Lake City. About 93% of the population is white and only 0.5% is black.

The attorney said that since news of Hunt's death was made public, they had received multiple calls from people with concerns about the city police. "They say 'I've been profiled', 'they pulled my kids over', 'anyone who doesn't fit in is given trouble'," said Edwards.

The city has 34 police officers, seven of whom work only part-time. Owen Jackson, a spokesman for the city, declined to provide details on the racial makeup of the force. Jackson said that the city regarded employees' race as "private" under state law "and not subject to disclosure".

Hunt's death was one of three fatal police shootings around the state of Utah in three days. However Tim Taylor, the deputy chief attorney for Utah county, said that police shootings in the county were rare. The only one in recent memory, he said, was the death of a carjacker with significant criminal history in January this year after he ambushed and killed a sheriff's sergeant.

Hunt died outside a Panda Express restaurant after fleeing up to 100 yards from his initial confrontation with police outside the bank, where prosecutors say he was first "shot at" by the officers. A witness standing in a gas station opposite has said she saw Hunt running away as she heard the first gunfire.

Edwards has said that the family's private autopsy shows that all six shots entered Hunt's body from behind. He said the deadly shot in Hunt's back did not have an exit wound. Citing a desire to shield the pathologist from media attention, Edwards has declined to identify him. "This is a very, very well respected pathologist in the state of Utah," he said.

An autopsy has also been carried out by a state medical examiner. Its findings have not been disclosed. Investigators have also obtained surveillance footage from cameras at both the bank, a branch of Cyprus Credit Union, and from the Panda Express restaurant. A spokeswoman for the bank said the drive-through forecourt, where Hunt and the officers were photographed shortly before the shooting, was watched by a camera.