Former Virginia governor Bob McDonnell, right, arrives at federal court in Richmond on Aug. 20 with attorney John Brownlee. McDonnell is now appealing his conviction on corruption charges. (Steve Helber/AP)

Federal prosecutors on Tuesday fired back at former Virginia governor Robert F. McDonnell’s claim that he deserves a new trial, saying that a federal judge properly instructed jurors and that many of the arguments that defense attorneys have raised are ones the judge had already rejected.

The filings from prosecutors in the Eastern District of Virginia were largely unsurprising, and U.S. District Judge James R. Spencer is likely to agree with them as he has, indeed, ruled in the government’s favor in similar disputes earlier. Still, the motions preview the government’s side of the battle that is likely to play out in a federal court of appeals. And they offered at least one new detail: The mysterious dismissal of a juror on the trial’s 12th day is part of the former first couple’s bid for new proceedings.

The McDonnells were convicted last month of lending the prestige of the governor’s office to Richmond businessman Jonnie R. Williams Sr. in exchange for $177,000 in loans, vacations and luxury goods. Prosecutors said that in return for Williams’s largesse, the couple arranged a meeting for the businessman with a state health official, allowed him to host an event at the governor’s mansion to promote his company’s dietary supplement and permitted him to invite guests to another mansion event that was intended for health-care leaders.

The McDonnells’ attorneys argued in filings soon after the verdict that their clients deserved to be acquitted — or at least be granted new trials — citing “numerous legal errors” in the proceedings that ultimately led to their conviction on public corruption charges.

In the filings Tuesday, prosecutors revealed — perhaps inadvertently — that McDonnell is also citing the dismissal of a juror on the trial’s 12th day as a reason he deserves a new trial. Discussions about Louis DeNitto — the dismissed juror who said publicly he would have pushed against convicting the McDonnells — have so far played out in sealed proceedings and filings.

A footnote at the end of nearly six pages of redacted material deals entirely with a dispute involving DeNitto, revealing that his dismissal is the subject of legal wrangling. In the footnote, prosecutors wrote of some sort of inquiry by the judge during the trial into DeNitto’s communications with a lawyer.

The parties seem to have discussed those communications at a secret hearing on the trial’s 12th day — when DeNitto was dismissed — although the exact nature of what was discussed or what is in dispute now is unclear. The footnote referenced another footnote in filings from McDonnell’s attorneys that seems to have been redacted.

The Washington Post has filed a motion asking the judge to unseal the material, arguing that it would be inappropriate to potentially overturn the verdict of a jury based on reasoning that has not been revealed to the public. U.S. Attorney Dana Boente declined to comment. The McDonnells’ attorneys did not immediately respond to phone and e-mail messages Tuesday night, nor did an attorney for DeNitto.

Also on Tuesday, prosecutors took particular aim at the defense’s contention that Spencer defined an “official act” too broadly for jurors, leading jurors to improperly convict the McDonnells of public corruption. Prosecutors were required to prove that the McDonnells performed or promised to perform “official” acts as part of a corrupt bargain with Williams.

The McDonnells’ attorneys had argued that the former governor and his wife merely facilitated Williams’s access to government officials but never lent or agreed to lend the actual power of the governor’s office to him. Prosecutors argued in their filings that Spencer interpreted the term “official” appropriately and that his definition was virtually the same as that in the public corruption prosecution of former congressman William J. Jefferson (D-La.).

They noted that the definition in that case withstood an appellate challenge.

“The only meaningful difference between that language from the Fourth Circuit’s Jefferson opinion and the Court’s instruction in this case is that this Court adjusted the language so as to remove the particular references to a congressman and the legislative process — an appropriate adjustment given that the defendant here was an executive rather than a legislator,” prosecutors wrote.

The McDonnells’ attorneys have also argued that jurors should not have been allowed to see evidence that McDonnell’s staffers discussed showing the governor where he could play golf for free, nor should jurors have been allowed to see that McDonnell accepted an expensive island vacation from a Henrico hotelier and failed to report it on state disclosure forms. Prosecutors said both were appropriate pieces of evidence and added that the discussions of free golf outings were used only to counter McDonnell’s testimony that he accepted gifts from Williams and others just to spend time with his family.

Prosecutors also argued that the judge was correct in not separating the trials for Robert and Maureen McDonnell and that Maureen McDonnell should not be acquitted of an obstruction of justice charge that she was convicted on alone.

Also on Tuesday, the McDonnells’ legal defense fund made a renewed e-mail pitch to prospective donors and encouraged them to write to the judge before the couple’s sentencing, now scheduled for Jan. 6.

Rosalind S. Helderman contributed to this report.