It responds to a sentencing memorandum filed earlier this week by Flynn's lawyers that suggested irregularities in how he was interviewed.
The memo is expected to emphasize the retired Army lieutenant general's three decades in the military, including five years in combat, and his acceptance of responsibility for his actions early on in the Russian Federation investigation.
"As the Government has made clear, his cooperation was not grudging or delayed", said the memo written by attorneys Robert Kelner and Stephen Anthony.
Cohen's sentencing underscores the scope and breadth Mueller's probe has taken as it's investigated the ties between Russian Federation and Trump's team, an examination that often has consumed the President for the first half of his term.
In a surprise move last week, Mueller recommended Flynn serve no prison time, citing his "substantial assistance" in the ongoing probe.
In total, Flynn met 19 times with the special counsel's office and others, for nearly 63 hours, they said.
The FBI interview took place on January 24, 2017, soon after Trump took office.
Prosecutors said Flynn had committed to a false story weeks before the January 24, 2017, interview with the FBI, having lied several times already to White House officials about his dialogue with ambassador Sergey Kislyak and then repeating those falsehoods to federal agents.
Since May of 2017, former FBI director Robert Mueller has led an investigation into Russian interference during the 2016 election.
DiGenova said Flynn knew that all of his conversations with the Russian ambassador were legal and nearly certainly being recorded by the government.
In December of that year, Flynn pleaded guilty to lying to the Federal Bureau of Investigation during the interview about contacts he had with Russia's ambassador to the U.S., Sergey Kislyak, during the presidential transition - from election day 2016 until President Donald Trump's inauguration. Around the same time, President Donald Trump's former attorney Michael Cohen pleaded guilty to eight federal charges. And Mueller said: 'Well, maybe he did.' And now they're all having a big dispute, so I think it's a great thing that the judge is looking into that situation. They say Manafort lied about his interactions with a longtime associate they say has ties to Russian intelligence, his contacts with Trump administration officials and other matters under investigation by the Justice Department. Now, many believe the agents were sent there to catch him in a perjury trap. Trump also plays a central role in a separate case in NY, where prosecutors have implicated him in a crime.
The document filed late Tuesday includes character references praising Flynn's 33-year military career, including four Bronze Stars and other recognition. "The Court should reject the defendant's attempt to minimize the seriousness of those false statements to the FBI", Mueller argued."The circumstances of the defendant's interview also show that his decision to make false statements was voluntary and intentional".