WASHINGTON/NEW YORK (Reuters) - 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. One of the senior officials said McMaster’s anger over the campaign “is known to the president” but declined to say whether the national security adviser had told Trump directly or through General John Kelly, an ally and the president’s new chief of staff. “McMaster isn’t saying Bannon is the mastermind behind the campaign, but he does think Bannon could stop it if he wanted to,” said one of McMaster’s defenders. In a television interview on Sunday, McMaster repeatedly declined to answer when asked if he could work with Bannon. About their feud, Bannon declined to comment and McMaster was unavailable for comment. Instead of firing Bannon, Trump could move McMaster into a position outside the White House, possibly back to an active military command role, or keep both men where they are and insist on some form of truce. Bannon has survived other White House power struggles this year and established a detente with Trump’s son-in-law and senior adviser Jared Kushner after a scolding from the president. The two senior officials who support McMaster said Kelly is angry that the anti-McMaster campaign has made the White House appear chaotic, reflecting badly on him as he was brought in as chief of staff two weeks ago to restore order and discipline. Bannon sees himself as the defender of Trump’s nationalist base and has advocated for both an end or renegotiation of trade deals and a more isolationist approach to foreign affairs than McMaster.  He has pushed to scrap the 2015 nuclear-weapons agreement with Iran, which McMaster argues should remain in place, and has also proposed using contractors to fight the war in Afghanistan rather than expanding U.S. forces there, as McMaster has advocated.  McMaster is part of a more pragmatic group that Bannon likes to label “globalists.” He drew the fury of Bannon’s supporters by recently overhauling the White House’s National Security Council, pushing out four staffers who were seen as close to Bannon. Conservative commentator Mike Cernovich is a Bannon ally and has been a vocal critic of McMaster, even leveling personal attacks against him. Cernovich says he does not talk directly to Bannon but praises him as an important counterweight to McMaster.  He also warns that the president would alienate his most loyal supporters if he fires Bannon. “I don’t think that people who like Trump are suddenly going to say, ‘We’re going to fight Trump.’ Instead they’ll say, ‘What’s the point of supporting him?’” Cernovich told Reuters. The conservative Jewish-American and pro-Israel group Zionist Organization of America (ZOA), which also has close ties to Bannon, has been one of McMaster’s sharpest critics, urging Trump to reassign him away from policy areas dealing with Israel and Iran.  Trump has himself backed McMaster, saying he was a “good man and very pro-Israel”. A source close to the ZOA bristled at the suggestion that Bannon was influencing its approach and said it would not tone down the campaign against McMaster, despite entreaties by Bannon  to do so. “We find it remarkably offensive that anyone would suggest that Steve Bannon or anyone else tells us what to say or what not to say,” the source said. “It makes me feel awful that he’s getting blamed for this, but there’s nothing I can do about it.” 