Speaking at a White House event on Friday, Trump said former army psychiatrist Nidal Hasan would be executed by firing squad.
But he made no comment on the plan announced by Secretary of Defense Pete Hegseth on Thursday.
Hegseth had earlier said it will be "public," telling TV outlet Real America's Voice: "We'll make sure that people are able to watch it."
Trump, who has approved the execution, told a rally in Texas on Wednesday that "we are going to deliver final justice to an evil killer".
The White House has directed all questions to the Pentagon.
US Vice President JD Vance cast doubt on Friday whether the Pentagon will live-stream the execution.
"I don't know that that's actually going to happen," Vance told reporters while campaigning in Ohio.
"If it's ultimately live-streamed, I'm not going to be watching it."
Vance added that Hasan's crimes should not be forgotten.
"So whatever the controversy is about the method of the execution, I hope that people don't forget that this is a guy who brutally murdered a lot of innocent people," Vance said.
Republican politicians and conservative strategists have criticised the plan for a public execution.
Republican Senator Thom Tillis of North Carolina called the idea "beyond disgusting" in a social media post.
"Public executions are what oppressive dictatorships like Iran and Afghanistan do," said the senator, a frequent Trump critic who is not running for re-election.
"It should not be happening in America."
Hasan is set to become the first person to be executed by US military firing squad since 1945.
The execution is scheduled for December 3 at the same sprawling Texas base where Hasan opened fire with a handgun in a medical facility.
with PA and AP
