"The president has a right to have White House staff who he is comfortable with... and in whom he has confidence," Rove, a former adviser to President George W. Bush, said on "Fox News Sunday."
"This is not about trust," Williams, a Fox News political analyst, fired back. "This is about payback. This guy is a decorated soldier and, as far as we know, truth-teller."
Vindman was escorted off White House grounds Friday, two days after Trump was acquitted in the Senate on the impeachment charges brought by the House last year over his dealings with Ukraine.
Also Friday, U.S. Ambassador to the European Union Gordon Sondland, who testified about Trump’s Ukraine dealings during the House impeachment hearings, said the president recalled him from his position.
Williams said the firings represented a disregard from Trump for "all laws that protect whistleblowers or people who speak truth about when they see corruption or malfeasance in government."
He added, "I think he's going after Vindman... in order to scare other people into silence in the future."
Rove called Williams' accusation "outrageous" and reiterated the importance of Trump trusting those working beside him.
After a fiery back-and-forth concerning the heart of the impeachment push -- Trump's 2019 phone call with Ukrainian President Volodymyr Zelensky, Rove appeared to meet Williams in the middle.
"I understand why he's [Trump] angry but the American people want to hear someone who said, 'You know what? It's over and I intend to move on,' and I don't think he served his cause well by angrily striking out," Rove said.
"The president had a moment to strike a great, 'I'm looking forward,' which I think would've been good for him politically and good for the country. But, I understand this is something he cares deeply about because he feels personally aggrieved by it."
He added, "I just wish he would've been able to tone that down and tone a lot up of, 'let's move forward.'"
Fox News' Chris Wallace contributed to this report.