He added the investigation would “to the extent it needs to” involve lawyers at the civil rights division.
The investigation was previously being led by the Homeland Security Investigations branch of Immigration and Customs Enforcement (ICE), the BBC’s US partner CBS News reported.
Two agents involved in Pretti’s shooting have been placed on administrative leave while the incident is investigated, the US Customs and Border Protection (CBP) said on Thursday.
According to a preliminary DHS report sent to Congress, two officers fired their weapons at Pretti during a scuffle. Initial official accounts had alleged Pretti brandished his gun.
The 37-year-old intensive care nurse, who was a US citizen, is understood to have joined protests in the city after Renee Good was shot dead by an ICE agent in Minneapolis on 7 January.
Their deaths sparked fresh demonstrations in the state, and prompted public outcry across the US and criticism from lawmakers in both parties.
Minnesota Governor Tim Walz and Minneapolis Mayor Jacob Frey have called for federal agents to be withdrawn entirely from the state’s capital region.
The state has also asked a federal judge to stop Operation Metro Surge, the DHS’s immigration enforcement initiative which began on 1 December and involves some 3,000 officers.
President Donald Trump has said his administration is “going to de-escalate a little bit” in Minnesota, while his border tsar Tom Homan said on Thursday that the administration planned to “draw down” federal forces if local officials co-operated.
“We are not surrendering our mission at all. We’re just doing it smarter,” Homan told a news conference in Minneapolis, without specifying what form a de-escalation might take.