Previous special counsel investigations, including probes of President Bill Clinton in the late 1990s, have also spent millions over a few months' time.
The bulk of those expenditures are on personnel, with $1.2 million spent on DOJ employees reassigned to Mueller's team and about $500,000 on others brought in on the investigation.
The special counsel's budget itself has not been made public.
Although the expenditures that took place between mid-May and September 30 for the special counsel's operations are relatively low compared with what many had anticipated, they could provide additional fodder for Republicans who have been critical of Mueller's work.
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Mueller was appointed special counsel in May, after President Donald Trump fired Federal Bureau of Investigation director James Comey. Dianne Feinstein of California, the top Democrat on the Judiciary Committee which is conducting its own investigation, said in a statement.
The four-and-a-half year investigations headed by Starr and his successor, Robert Ray, cost more than $52 million in taxpayer funds as they probed Clinton and then-first lady Hillary Clinton.
Mueller's spending "is entirely reasonable given the results we've already seen", Sen.
So far, the probe has resulted in two indictments and two guilty pleas, none of which are in any way related to charges of "links and/or coordination" with Russian Federation. An additional $3.5 million was paid out by the Justice Department to support the investigation, though the special counsel's office says that money would have been spent on ongoing probes anyway, even if Mueller had not been appointed.
Since the probe began in May, the special counsel has charged four people, two of whom have pleaded guilty. Mueller also disclosed that he secured a guilty plea from George Papadopoulos, who was a junior foreign-policy adviser to the Trump campaign, for lying to the Federal Bureau of Investigation about contacts with Russian operatives.