According to Saturday's memo outlining the changes, both leaders will now attend NSC Principals Committee meetings only when "issues pertaining to their responsibilities and expertise are to be discussed."
"Pushing them out of the National Security Council [Principals Committee] meetings except when their specific issues are at stake is a big mistake," said Gates, who served as defense secretary for Presidents George W. Bush and Barack Obama.
White House press secretary Sean Spicer defended giving Bannon a seat at the Principals Committee meetings, saying on "This Week," "Having the chief strategist for the president in those meetings — who has a significant military background to help make, guide what the president's final analysis is going to be — is crucial."
Spicer added that Bannon is a former Navy officer who has "a tremendous understanding of the world and the geopolitical landscape that we have now."
"That's clearly inappropriate language from a former ambassador," Spicer responded on "This Week."
"We are instilling reforms to make sure that we streamline the process for the president to make decisions on key, important intelligence matters," he said. "What they have done is modernize the National Security Council so that it is less bureaucratic and more focused on providing the president with the intelligence he needs."
Editor's Note: An earlier version of this story indicated that under the president's signed memorandum, the director of national intelligence and chairman of the Joint Chiefs of Staff would be limited in attending National Security Council meetings. As Martha Raddatz stated on "This Week," it is the National Security Council Principals Committee meetings to which their attendance will be limited. In addition, White House chief strategist Stephen Bannon now also has a seat at National Security Council Principals Committee meetings.