(CNN) President Donald Trump further reorganized the National Security Council on Monday after he came under sharp criticism for ousting the country's most senior intelligence and military officials as regular members of the Principals Committee -- and installing one of his top political advisers on the key panel.

On Monday, White House spokesman Sean Spicer announced that Trump will reinstate the director of the CIA as a regular Principals Committee member. But the President will keep his chief strategist, Stephen Bannon, as a regular committee member -- a move that came under fire -- while the director of national intelligence and the chairman of the Joint Chiefs of Staff will not be regular attendees.

The committee is a Cabinet-level group of agencies focused on national security that was established by President George H. W. Bush in 1989.

Former acting CIA chief Michael Morell on Monday sharply criticized the move to add Bannon to the group while limiting the involvement of the chairman of the Joint Chiefs and DNI, calling it "unprecedented" in an appearance on "CBS This Morning."

"I have never been to a principals' meeting where the views of the DNI and the views of the chairman are not relevant," said Morell, who advised Hillary Clinton's campaign for president. "Every principals' meeting starts with an intelligence briefing by the DNI."

He added, "Having somebody like Bannon in the room brings politics into a room where there should be no politics."

Vermont Sen. Bernie Sanders tweeted that the move was "dangerous" and called for Bannon to be removed from the panel.

"Steve Bannon sitting on the National Security Council is dangerous and unprecedented. He must be removed," Sanders said.

Spicer claimed the move was in line with previous administrations' steps to structure their own NSCs, and said that the chairman of the Joint Chiefs of Staff and the director of national intelligence would both be welcome to attend any NSC session.

The CIA director is a Trump ally, and subordinate to the director of national intelligence on organization charts.

Pentagon spokesman Capt. Jeff Davis said the NSC set-up under President George W. Bush was similar.

"There's been no change effectively to the role of the chairman in 16 years," Davis said, referring to the chairman of the joint chiefs of staff. "What has remained constant is the role of the chairman. He is the principal military adviser to the secretary, he is the principal military adviser to the president."

Davis said the defense secretary "intends to always have the Chairman at his side when he is discussing anything that has anything to do with our national security or our military," whether he's engaging with the full National Security Council or the Principals Committee.

"We don't see this as a change, we see this as a continuation of the very critical role that the chairman has played in an advisory capacity," Davis said.

Spicer hammered President Barack Obama's National Security Adviser Susan Rice for asking on Twitter why the CIA was omitted from the NSC, noting that Obama's own NSC memo from 2009 didn't list the CIA.

In a series of tweets in which she described the reorganization as "stone cold crazy," Rice had tweeted: "Chairman of Joint Chiefs and DNI treated as after thoughts in Cabinet level principals meetings. And where is CIA?? Cut out of everything?"

To date, every version of the Committee has included the Joint Chiefs chairman and the director of the CIA or, once it was established, the head of the DNI. DNI James Clapper was always included in Obama administration's NSC principals' meetings, CNN confirmed.

Bannon's presence reinforces the notion he is, in essence, a co-chief of staff alongside Chief of Staff Reince Priebus, and demonstrates the breadth of influence the former head of Breitbart News has in the Trump administration.

Sen. John McCain, R-Arizona, offered praise for the administration's national security team, but he expressed serious concerns about Bannon.

"I think the national security team around President Trump is very impressive," McCain said Sunday on CBS' "Face the Nation."

"I am worried about the National Security Council who are the members of it and who are the permanent members of it," McCain added. "The appointment of Mr. Bannon is something which is a radical departure from any National Security Council in history. It's of concern this ... reorganization."

The NSC is run by National Security Adviser Michael Flynn, a former head of the Defense Intelligence Agency until he was asked to step down in 2014 by senior intelligence leaders.

There has been running tension between the Trump administration and the intelligence community, though during a visit to the CIA Trump declared that "nobody feels stronger about the intelligence community than Donald Trump ... I love you. I respect you."

Before then, the President had argued that intelligence services were politically partisan, he dismissed their findings that Russia hacked Democratic targets during the campaign and referred slightingly to the intelligence community by tweeting with the word intelligence in quotes.

In setting out the reorganization, Trump said that "security threats facing the United States in the 21st century transcend international boundaries. Accordingly, the United States Government's decision-making structures and processes to address these challenges must remain equally adaptive and transformative."

Regular members of the Principals Committee will include the secretary of state, the treasury secretary, the defense secretary, the attorney general, the secretary of Homeland Security, the assistant to the President and chief of staff, the assistant to the President and chief strategist, the national security adviser and the Homeland Security adviser.