Special counsel Robert S. Mueller III’s investigation cost the Justice Department about $6.7 million in his first 4½ months in office, according to a report released by the department Tuesday. (Charles Dharapak/AP)

Special counsel Robert S. Mueller III’s investigation of possible coordination between the Trump campaign and Russia to influence the 2016 election cost the government about $6.7 million in Mueller’s first 4½ months in office, according to a report released by the Justice Department on Tuesday.

The price tag is likely to rile Republicans who have been critical of Mueller’s team and wary of a long and costly investigation, though independent counsels have in the past spent tens of millions of dollars on lengthy probes.

Mueller’s spending included $3.2 million in direct and reimbursed expenditures, including more than $1.7 million for personnel, $733,000 for equipment, $362,000 for rent and utilities, $223,000 for travel, and $157,000 for contract services, such as technology services and transcripts, according to the report. That represents new money coming from an indefinite appropriation for independent counsels, which the Justice Department determined could be used to fund Mueller’s work.

Mueller’s probe also caused other Justice Department components to spend about $3.5 million on work attributable to the special counsel investigation, according to the report. The report said that past special counsels did not report such expenditures and that the expenses would have been incurred “irrespective of the existence” of the special counsel’s office.

Mueller was appointed special counsel in May, after President Trump fired FBI director James B. Comey. The Justice Department’s report covered the period from May 17 to Sept. 30.

Though Mueller’s investigation is not yet a year old, his team of prosecutors has made significant moves. Mueller’s 17 lawyers — some reassigned from within the government and others brought in from private practice — have charged or negotiated plea deals with four former Trump campaign or administration officials, including former campaign chairman Paul Manafort and former national security adviser Michael Flynn.

Manafort was charged, along with his longtime business partner Rick Gates, for work on behalf of Ukraine unrelated to the campaign. Flynn pleaded guilty to lying to the FBI about his contacts with Russia’s ambassador during the transition period and, in a potentially ominous sign for the White House, agreed to cooperate with Mueller.

Though Flynn has already admitted that other top transition officials — including Jared Kushner, the president’s son-in-law, and K.T. McFarland, who is now nominated to be the U.S. ambassador to Singapore — were aware of his Russia-related dealings, Mueller is likely to want to talk to him about a wider range of topics, including whether Trump obstructed justice and tried to short-circuit the probe.

Trump has in the past taken aim at Mueller’s hires, citing some team members’ political contributions to Democrats, including Hillary Clinton. More recently, though, he has highlighted news reports that Peter Strzok, the former top FBI official assigned to the investigation, was reassigned after it was discovered that he and another team member had exchanged texts disparaging Trump and supporting Clinton.

Strzok was also a key figure in the probe of Clinton’s use of a private email server while she was secretary of state.

“Report: ‘ANTI-TRUMP FBI AGENT LED CLINTON EMAIL PROBE’ Now it all starts to make sense!” Trump wrote on Twitter.

White House lawyers declined to comment on Mueller’s expenditures.

Lawrence E. Walsh, the prosecutor who investigated Reagan officials in the Iran-contra affair, spent $47.4 million during his eight-year investigation. Former independent counsel Kenneth W. Starr spent more than $52 million investigating President Bill Clinton, and the five independent counsels appointed to look into various Clinton-related matters during the 1990s spent more than $100 million.