For months, U.S. President Donald Trump's national security adviser and his chief strategist have battled for influence behind the scenes, and their feud may force another shake-up at the White House.

The dispute between Lieutenant General H.R. McMaster and political strategist Stephen Bannon has reached a level of animosity that is destabilizing Trump's team of top advisers just as the administration tries to regain lost momentum, three senior officials said.

Under pressure from moderate Republicans to fire Bannon, Trump declined to publicly back him on Tuesday, although he left his options open. "We'll see what happens with Mr. Bannon," he told reporters at Trump Tower in New York.

Whatever Trump decides could chart the fate of a nuclear-weapons deal with Iran, U.S. troop deployments to Afghanistan and White House staffing decisions — all issues over which Bannon and McMaster have sparred.

Bannon has been in a precarious position before but Trump has opted to keep him, in part because his chief strategist played a major role in his election victory and is backed by many of the president's most loyal rank-and-file supporters.

"The president obviously is very nervous and afraid of firing him," a source close to the White House told Reuters.

The source floated the possibility that Bannon could be demoted instead of fired, noting that he might turn into a harsh critic of the administration if he is forced out of the inner circle.

Two other senior officials, both supporters of McMaster who asked not to be identified, said he blames Bannon for a series of attacks against him by right-wing website Breitbart News, which Bannon used to lead, and other far-right conservative groups.

In recent weeks, Breitbart has published a series of articles making a case for McMaster's ouster on the basis that he is not a strong ally of Israel and that he has staffed the National Security Council with holdovers from the Obama administration.