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Robert Harward was deputy commander at Central Command, which oversees military operations in the Middle East and north Africa. Image Credit: Reuters

President Donald Trump, scrambling to find a new top security aide after firing his first one and being spurned by another candidate, said on Friday he has four people under consideration for the job, including acting national security adviser Keith Kellogg.

Trump ousted Michael Flynn on Monday in a controversy over the retired lieutenant general's contacts with Russia, and on Thursday retired Vice Admiral Robert Harward turned down the Republican president's offer to replace Flynn.

Trump said in a post on Twitter on Friday he was weighing four potential candidates for national security advisor.

"General Keith Kellogg, who I have known for a long time, is very much in play for NSA - as are three others," he said without naming the other candidates.

Kellogg, a retired lieutenant general who currently is chief of staff of the White House National Security Council, stepped into the national security adviser role on an acting basis after Flynn's firing.

Retired General David Petraeus, who held key command posts in the wars in Iraq and Afghanistan and served as CIA director under former President Barack Obama, also had been mentioned by a White House official as a replacement for Flynn earlier.

Petraeus quit as CIA chief in 2012 and pleaded guilty to a misdemeanor charge of mishandling classified materials relating to documents he had given his biographer, with whom he had an affair.

NBC News reported two other retired military officers were also under consideration: General James Jones, former supreme allied commander in Europe who served as national security adviser to Obama from 2009 to 2010; and General Keith Alexander, former U.S. National Security Agency chief.

Harward, a senior executive at Lockheed Martin and former Navy SEAL, declined Trump's offer in part because he wanted to bring in his own team, according to two sources familiar with Harward's decision.

The White House chief of staff, Reince Priebus, told Fox News on Friday that Harward's family "didn't sign off" on him taking the job.

"That's all it is," Priebus said.

Flynn, a close adviser to Trump during his presidential campaign last year, was seen by Moscow as a leading advocate of friendlier ties with Russia.

Trump said on Thursday he fired Flynn because he had misled Vice President Mike Pence about conversations he had with the Russian ambassador to the United States about sanctions imposed by President Barack Obama's administration before Trump took office. Trump has defended Flynn's actual contact with the ambassador, saying what he did "wasn't wrong."

The Washington Post reported on Thursday that Flynn told FBI agents last month that he had not discussed sanctions against Russia with the ambassador before Trump took office. Flynn's Jan. 24 interview with the FBI could expose him to charges, since lying to the agency is a felony, but any decision to prosecute would lie with the Justice Department.

Obama imposed the sanctions on Russia on Dec. 29 after U.S. intelligence agencies concluded Russia hacked and leaked Democratic emails during the election campaign as part of an effort to tilt the vote in Trump's favor.

Trump on Thursday repeated his interest in closer ties with Russian President Vladimir Putin's government, saying "I would love to be able to get along with Russia" but that "it's possible I won't be able to get along with Putin."