A rankled Trump declared on Twitter on Thursday that "The Navy will NOT be taking away Warfighter and Navy Seal Eddie Gallagher's Trident Pin."
On Saturday, however, a senior Pentagon official who requested anonymity in order to speak freely said the "peer review board is proceeding."
Whether Gallagher can remain in the unit or not will be determined by a panel of Navy SEAL officers that is set to convene in December.
The move came as multiple US news outlets reported that Navy Secretary Richard Spencer had threatened to resign over the affair, a claim he sharply denied.
"Contrary to popular belief, I am still here. I did not threaten to resign," Spencer said, speaking at a forum in Halifax, Canada.
The US Navy chief said he did not consider Trump's tweet to be a formal order. "I need a formal order to act," Spencer told reporters on the sidelines of the forum.
According to the US Constitution, the president is the commander-in-chief of the country's armed forces.
Gallagher, a 15-year Navy SEAL, had been accused in the stabbing death of a wounded Islamic State prisoner in Iraq in 2017, attempted murder of other civilians and obstruction of justice. 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.
As a result, he was demoted one rank, from chief petty officer to petty officer first class.
Gallagher's case had been championed by Fox News, which the president follows closely.