U.S. President Donald Trump ordered the Pentagon not to remove Chief Petty Officer Edward Gallagher, a Navy SEAL at the center of a war crimes case, from the elite unit, the Defense Secretary said on Monday.

Gallagher was acquitted of a murder charge in the stabbing death of an ISIL militant captive, but a military jury convicted him of posing with the corpse while in Iraq in 2017. He was then demoted to chief.

According to Esper, President Trump gave a formal order on November 15 to halt the military's plans to hold a review board.

"I spoke with the President on Sunday. He gave me the order that Eddie Gallagher will retain his Trident pin," Esper told reporters at the Pentagon, referring to Special Operations Chief Edward Gallagher.

Esper said he had been in favor of following the regular processes but stressed that, as president, Trump had "every right, authority and privilege to do what he wants to do".

Esper's comments were the first since he fired Navy Secretary Richard Spencer on Sunday over his handling of Gallagher case.

Esper gave new details on Monday about why he fired Spencer, saying the Navy chief had sought to cut a side deal with the White House that was "contrary to what we had agreed to and contrary to Secretary Spencer's public position," in which he appeared to favor allowing the military justice process to go ahead.

"We learned that several days prior, Secretary Spencer had proposed a deal whereby if the President allowed the Navy to handle the case, he would guarantee that Eddie Gallagher would be restored to rank, allowed to retain his Trident and permitted to retire," Esper said.

Gallagher's case had been championed by conservative commentators, who argued he had been treated unfairly.

Trump restored his rank earlier this month, when he also pardoned two Army officers accused of war crimes in Afghanistan. On November 15, he issued executive clemency directives for Army 1st Lt. Clint Lorance and Army Maj. Matthew Goldsteyn and directed that Gallagher's pay grade be restored to E-7.

People have questioned that the action shows the president has intervened in the case of Gallagher and critics, including Democrats in Congress, have said such actions would undermine military justice and send a message that battlefield atrocities will be tolerated.

Trump defended himself on Monday, saying he was sticking up for "warriors" and defending the military.

(With input from Reuters, AFP)