"Contrary to popular belief, I'm still here. I did not threaten to resign", Spencer said, cited by Reuters. Earlier, Spencer recommended that Gallagher face a special commission to rule on whether Gallagher could keep his elite rank.
Last week, Trump intervened in the case, ordering the US Navy to restore Gallagher's Navy SEAL rank, and clearing the way for him to retire with a full pension.
Trump also pardoned Army First Lieutenant Clint Lorance and Army Major Mathew Golsteyn, separately accused of war crimes, along with attempting to reinstate Gallagher's rank.
On Thursday, Trump lashed out at the criminal proceedings, tweeting: "The Navy will NOT be taking away Warfighter and Navy Seal Eddie Gallagher's Trident Pin. This case was handled very badly from the beginning. Get back to business!"
Gallagher had been demoted following a July conviction for posing in a photograph alongside the body of a dead militant fighter during the former's 2017 deployment in Iraq. The US soldier was cleared of murder charges after he had fatally stabbed the enemy fighter in the photo.
According to media reports, if Gallagher loses his SEAL rank, he would be forced to either retire or find a different position in the military. Gallagher's defence team claimed that the move to remove Gallagher from the SEALs was driven by Naval Special Warfare Commander Rear Admiral Collin Green, Reuters reported Wednesday.
Gallagher would have faced a life sentence if had he been convicted for the murder.