Not everyone is convinced that President Trump wrote, or even glimpsed at, a statement in which he defends National Security Adviser H.R. McMaster following accusations that he was trying to undermine Trump's agenda and calls for his ouster.

"General McMaster and I are working very well together. He is a good man and very pro-Israel. I am grateful for the work he continues to do serving our country," Trump said in a statement Friday.

Two leading figures in the far-right movement, who had been supporting the campaign to remove McMaster and have singled him out for being behind White House leaks, say its bogus.

"Who knows if [Trump] even saw the statement put out in his name?", longtime Trump confidant and political trickster Roger Stone pondered on Twitter. He later added a more certain: "McMaster must go - Statement of support put out by WH was never seen or approved by [Trump]."

His sentiments are echoed by far-right blogger Mike Cernovich, who mentioned the hashtag #FireMcMaster which went viral last week. "Trump responds to #FireMcMaster in a statement that sounds nothing like his voice," Cernovich said. Hundreds of accounts linked to Russia have promoted the idea of firing McMaster via the hashtag.

Cernovich, who has long been critical of McMaster and his allies, has created a website called McMasterLeaks.com, which seeks to gain damaging information on McMaster.

Both Stone and Cernovich regularly appear on Infowars, which has a reputation of spreading conspiracy theories like "Pizzagate."

Part of the statement attributed to Trump, mentioning how McMaster is "very pro-Israel," appears to be in response to stories posted this week by right-wing outlets like Brietbart News, which White House chief strategist Steve Bannon used to run, asserting McMaster is hostile to Israel.

McMaster reportedly rocked the West Wing last week by shaking up his national security team, letting go of members favored by the nationalist sect in the White House, led by Bannon. Of particular note, McMaster initiated the ouster of Ezra Cohen-Watnick, the senior director for intelligence programs at the National Security Council, and the latest ally of former National Security Adviser Mike Flynn to be dismissed from the White House. The move came after McMaster previously failed to fire Cohen-Watnick in March, being blocked due to the efforts of Bannon and Jared Kushner, the president's son-in-law and senior adviser.

McMaster telling former Obama national security adviser Susan Rice in April that she would continue to have access to classified information was seen as deepening the rift between him and Bannon. The two are also said to be butting heads on foreign policy matter, including U.S. strategy in Afghanistan.

A report came out this week that Trump is mulling sending McMaster to Afghanistan to lead the U.S. war effort there, and replace him in the national security adviser position with CIA Director Mike Pompeo.

But, beyond Trump's statement of confidence in McMaster, his new chief of staff, John Kelly, also reportedly supports the idea of keeping McMaster where he is.