WASHINGTON—Mike Flynn should have known not to lie to federal investigators early last year about his interactions with Russians, the special counsel’s office said Friday, dismissing a suggestion that the former Trump aide hadn’t been warned that lying to the FBI is a crime.

Lawyers for Mr. Flynn, who has been cooperating with the special counsel investigation for more than a year, had asked a federal judge considering his sentence to take into account agents’ failure to warn him that lying to the Federal Bureau of Investigation is a crime before he was interviewed in January 2017.

That suggestion drew a rebuke in Friday’s sharply worded court filing from the office of special counsel Robert Mueller, which has otherwise been supportive of Mr. Flynn’s request for leniency from the judge. The special counsel’s office has already requested no jail time for Mr. Flynn, who briefly served as President Trump’s national security adviser before he was ousted over his conflicting statements about the contacts with Russia.

“A sitting national security advisor, former head of an intelligence agency, retired lieutenant general, and 33-year veteran of the Armed Forces knows he should not lie to federal agents,” Mr. Mueller’s prosecutors wrote, citing some of Mr. Flynn’s credentials. “He does not need to be warned it is a crime to lie to federal agents to know the importance of telling them the truth.”

In Mr. Flynn’s own memo, filed earlier this week, his lawyers quoted an internal FBI memo saying the Bureau “decided the agents would not warn Flynn that it was a crime to lie during an FBI interview because they wanted Flynn to be relaxed, and they were concerned that giving the warnings might adversely affect the rapport.”

No warning is necessary to bring a prosecution for false statements, but the FBI often cautions witnesses that lying is a prosecutable offense.

Prosecutors’ Friday filing said Mr. Flynn began lying about his interactions with Sergey Kislyak, then the Russian ambassador to the U.S., as early as Jan. 13, 2017, when he had a subordinate tell a journalist that the two hadn’t discussed U.S. sanctions against Russia that had been levied by the Obama administration.

Mr. Flynn went on to mislead Vice President-elect Mike Pence, as well as the incoming White House chief of staff and press secretary, all of whom later made false statements on national television thanks to Mr. Flynn’s denials, the Mueller team noted.

“By the time of the FBI interview, the defendant was committed to his false story,” prosecutors wrote. Mr. Mueller, himself a former FBI director, wasn’t appointed as special counsel until May 2017, several months later.

Attempting to bolster their assertions, the special counsel’s team attached memos from former FBI Deputy Director Andrew McCabe and ex-FBI agent Peter Strzok. Both have since been dismissed from the bureau, Mr. McCabe for allegedly lying to investigators about his media contacts and Mr. Strzok over text messages that were critical of Mr. Trump.

The McCabe memo described how the FBI’s interview of Mr. Flynn on Jan. 24, 2017, came about. Mr. McCabe recounted that he called Mr. Flynn and explained that agents needed to speak to him about his interactions with Mr. Kislyak. Mr. Flynn agreed to be questioned without a lawyer present, and he expressed concerns about how details of his call had leaked to the media.

Mr. Mueller’s team on Friday didn’t reverse its view that Mr. Flynn deserves leniency. Federal law makes it a crime to make false statements to federal investigators, whether a person is under oath or not.

Mr. Trump and some of his Republican allies, who have sought to undercut the federal probes that have ensnared several of the president’s top aides, have suggested the FBI mishandled Mr. Flynn’s case. This past week, Mr. Trump suggested, without substantiation, that the recommended lighter sentence for Mr. Flynn indicated that Mr. Mueller had botched the case.

“They gave General Flynn a great deal because they were embarrassed by the way he was treated,” Mr. Trump said in a tweet this week. “They want to scare everybody into making up stories that are not true by catching them in the smallest of misstatements.”

Mr. Mueller’s prosecutors have said Mr. Flynn deserves leniency because of his long military service and extensive cooperation with investigators since pleading guilty a year ago.

Write to Byron Tau at byron.tau@wsj.com