Several Republican lawmakers criticised the move championed by Defense Secretary Pete Hegseth, while a top US Catholic bishop called the plan "barbaric" and former US officials said a livestream of the execution would hand terrorists a recruiting tool.
"I don't know that that's actually going to happen," Vance told reporters on Friday.
Vance added that if a livestream of the execution scheduled for December 3 occurs, "I'm not going to be watching it."
His comments raise questions about the extent of opposition within President Donald Trump's administration to the Pentagon's plans to livestream the execution of Nidal Hasan, who was found guilty in a US military trial of killing 13 people at Fort Hood in Texas.
Trump said at a White House event that Hasan deserves the death penalty by firing squad, calling him "a maniac". The Republican president has not said whether he thinks the event should be shown on a livestream.
A senior White House official said Trump "doesn't oppose the idea" of a livestream, but his position was not yet final and he could change his mind.
Death penalty experts said it would mark the first known broadcast or livestream of a lawful execution.
Hegseth, a Trump appointee, said on Thursday the public nature of the execution would demonstrate "there's serious consequences for these types of things."
Hegseth reposted a comment Trump made in 2013, possibly about the Boston Marathon bombers, saying: "Should be public execution for all to see — you will end this bullshit fast!"
The Pentagon on Friday declined to say whether families of those killed in Hasan's attack would be invited to attend the execution, as is common practice in civilian executions.
It remains unclear how the Army would select the shooters and what protocols might be followed during the execution itself. The Pentagon said it would release details later.
A top US Catholic official condemned the plan.
"This decision is a barbaric promotion of a culture of death and must be reconsidered," said Archbishop Paul Coakley, president of the United States Conference of Catholic Bishops.
Hasan is set to become the first person to be executed by firing squad by the US military since 1945. Hasan, an American-born Muslim, said during his 2013 trial that he carried out the shootings to try to stop what he called a US war on Islam.
"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 told reporters.
Joe Kent, who resigned this year as Trump's head of the National Counterterrorism Center, said the effort to deter extremism could backfire.
"Streaming his execution is not just a stain on our morality — it also gives the terrorists free propaganda that they will use to radicalize & recruit more terrorists," Kent wrote on social media.
Several Republican lawmakers urged the administration not to livestream the execution.
US law prohibits the recording or broadcasting of executions in the federal prison system. Military regulations have not applied that same prohibition.
Courts have rejected lawsuits brought by media organisations seeking broader public access to executions.
The UN human rights office said public executions violate prohibitions against torture.
The execution is scheduled to be held at the same sprawling military base where Hasan opened fire with a handgun in a medical facility. A military jury sentenced Hasan to death after finding him guilty of 45 counts of premeditated murder and attempted premeditated murder.
The shooting came weeks before Hasan, now 56, was scheduled to be deployed with US forces to Afghanistan. Hasan was left partially paralyzed and confined to a wheelchair from being shot by police during his arrest.
The last known executions by US military firing squads were in 1945, according to the Death Penalty Information Center.
with PA and AP
