"General McMaster and I are working very well together", he said in a statement.
The Times noted that Frank Gaffney Jr., president of the Center for Security Policy, had called McMaster "insubordinate to his commander in chief" in areas such as Islamic terrorism.
A senior White House official also told the New York Times that McMaster still has Trump's "total confidence", but that shouldn't be taken very seriously.
In a volley of attacks from right-wing media, McMaster has been accused of being anti-Israel, having a short temper and collaborating with Obama-era officials.
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Mr Trump had recently pondered a different role for General McMaster.
Conservative outrage has grown after it was revealed McMaster allowed Susan Rice, President Obama's National Security Advisor, to keep her security clearance.
But for now, at least, the campaign has not been able to convince Trump that he should get rid of McMaster, nor has it convinced Kushner, who was a staunch ally of the latest official McMaster pushed out of the NSC: senior director for intelligence Ezra Cohen-Watnick.
U.S. National Security Adviser H.R. McMaster and Israeli Defense Minister Avigdor Lieberman, May 2017.
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President Donald Trump has struggled to form a coherent policy in Afghanistan, in spite of H.R. McMaster's attempts to educate the president on the ongoing conflict, according to a new report from The Washington Post.
Under the law, and under certain conditions, it is common practice for some senior government officials to be given the unfettered access to classified information, and their "need to know" is waived under "Executive Order 13526 Section 4.4 Access by Historical Researchers and Certain Former Government Personnel".
McMaster's various moves have been noticed by Trump's base, with #FireMcMaster becoming a trending hashtag on Twitter, and a regular topic on conservative news sites - including Breitbart News. His allies bashed both Bannon and his "protege" Sebastian Gorka for trying to diminish McMaster's control over the NSC. And what do you do when a Chinese chatbot say it wants to go to American when asked what its dream was?
The firing of the NSC's director for strategy planning, Richard Higgins, on July 21, meanwhile, was linked to a conspiratorial memo he'd sent about radical Islam rather than his ties to Bannon or NSC aide Sebastian Gorka, an NSC aide said.
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The biggest problem McMaster faces is going up against Bannon, who sees Trump as a revolutionary official who will change the world after a cataclysmic event that ushers in the "fourth turning." But the White House officials told Circa that under the current congressional investigation, and given President Trump's ongoing concern that members of his team were unmasked, Rice's clearance should have been limited to congressional testimony only or revoked until the end of the investigation.