Green ordering the review "crossed a very risky line, having our uniformed flag officers being directly defiant of our commander in chief", Parlatore told CNN Thursday.
Gallagher came under court martial in 2018 on charges including premeditated murder, attempted murder, and aggravated assault with a unsafe weapon on non-combatants.
In July, he was acquitted of charges related to those accusations, but was convicted of a lesser charge - posing with the slain fighter's body in a group picture with other SEALs.
The New York Times reported Saturday that Spencer and Rear Adm. Collin Green, the admiral overseeing the SEALs, threatened to resign over the possible intervention by Trump. Trump, meanwhile, continued to tweet his support for Gallagher.
Navy Secretary Richard V. Spencer, denied the report. He added: "This case was handled very badly from the beginning". "I don't interpret them as a formal order". Earlier Saturday, Chief Navy spokesman Rear Adm. Charles Brown told CNN that those comments from Spencer "are in line with current White House guidance".
"I believe the process matters for good order and discipline", he told a reporter while at a conference in Halifax, Canada. "Contrary to popular belief, I'm still here and I did not threaten to resign", Spencer said.
Gallagher's lawyers have accused the Navy of trying to remove the SEAL designation in retaliation for Trump's decision last week to restore Gallagher's rank.
The Times also reported that military higher-ups are looking for a "face-saving compromise" with the president regarding the matter and are looking to convince Trump to change his mind.
Administration officials said they now hoped that Mr. Trump would allow the proceedings to continue, but it is unclear whether the president will do so.
Speaking Sunday with Fox News host Pete Hegseth, Gallagher had a chance to thank Trump directly for repeatedly intervening on his behalf.
This would seem to have defused a conflict between the president and Navy leaders, although it remained possible that Trump could still use his authority as commander in chief to intervene in the volatile and politically charged Gallagher case, despite assurances received by the Navy. It would include one SEAL officer and four senior enlisted SEALs, according to the two US officials.
Mr Gallagher can appear once before the board on December 4 but without his lawyers. He can call witnesses, and he can appeal the final decision of the board if it goes against him.
The firing was a dramatic turn in a long-running controversy involving Navy Chief Petty Officer Edward Gallagher, whose case has been championed by President Donald Trump.
"With the timing, it's hard to see how this was anything but a direct, public rebuke to the president", Mr. Parlatore said.