Robert Harward was widely tipped for the post after President Trump fired Michael Flynn on February 13.
A White House official said Robert Harward cited family and financial commitments, but media said the sticking point was he wanted to bring in his own team.
Michael Flynn had misled VP Mike Pence over his conversations with Russia’s ambassador to the US.
The latest setback emerged hours after Donald Trump robustly denied media reports of White House disarray, insisting in a news conference that his administration was running like a “fine-tuned machine”.
The White House is expected to name its new communications director on February 17, and media say the job will go to Mike Dubke, the founder of Republican media group Crossroads Media.
Robert Harward told the Associated Press the Trump administration was “very accommodating to my needs, both professionally and personally”.
“It’s purely a personal issue,” added the 60-year-old former Navy Seal who is currently based in Abu Dhabi as an executive for US defense contractor Lockheed Martin.
Asked about reports that he had asked to bring in his own staff at the National Security Council, Robert Harward said: “I think that’s for the president to address.”
Michael Flynn, a retired army lieutenant-general, was ousted amid claims that before he was even appointed as national security adviser he had discussed sanctions with a Russian envoy.
This would have potentially breached a law banning private citizens from engaging in diplomacy.
Michael Flynn initially denied having discussed sanctions with Sergei Kislyak, Moscow’s ambassador to Washington.
However, on February 13, President Trump asked for his resignation following revelations that Michael Flynn had misled the vice-president about his conversations with the diplomat.
Leading Republicans have called for an investigation into intelligence leaks that led to Michael Flynn’s resignation.
Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…