Trump steps up search for America's next top diplomat

President-elect Donald Trump (L) shakes hands with Mitt Romney after their meeting at Trump International Golf Club. (AFP/Drew Angerer)

Trump's quest for America's next top diplomat, the most prestigious position in the cabinet and the statesman who will have to grapple with foreign crises and wars, has been mired in internal divisions.

Each candidate offers different merits and drawbacks, making it a hefty decision for a 70-year-old maverick New York real estate tycoon, who has never previously held office.

On Tuesday the president-elect has scheduled meetings with Romney, the failed 2012 Republican White House nominee whose consideration has had Trump's inner circle up in arms, and Corker, chairman of the Senate Foreign Relations Committee.

Analysts say that picking Romney would reassure the Republican establishment and US allies worried about Trump's foreign policy.

Trump's meeting will be his second with the former Massachusetts governor, who castigated Trump during the election campaign as a "fraud" and a "conman," and refused to endorse him.

Top aide Kellyanne Conway - unusually for a senior political advisor - publicly aired her concerns about Romney, saying she had received "a deluge" of concern from supporters and stressing his past animosity towards Trump.

Outspoken former New York mayor Rudy Giuliani, who campaigned tirelessly for Trump, has been another early contender, but scrutiny over business dealings has since raised questions that could potentially disqualify him.

Petraeus, the most celebrated general of his generation, a former CIA director and former commander in Iraq and Afghanistan, has emerged latterly as a potential candidate despite a stunning fall from grace four years ago.

PETRAEUS 'PREMATURE'

He met the president-elect for an hour in New York on Monday, after which the president-elect sounded positive, tweeting: "Just met with General Petraeus - was very impressed!"

But Trump spokesman Jason Miller told Fox News Radio on Tuesday that it "might be a little bit premature" to assume Petraeus is being considered.

"There was a lot of getting to know you and see where General Petraeus might be able to be an asset, a team member, whether that's internally in the administration or whether it's on the outside," Miller said.

The 64-year-old scholar-warrior, who masterminded the widely credited surge in Iraq from 2008-2010, certainly has a depth of experience in world affairs unmatched by any of the other candidates known to be under consideration.

But in 2012 he resigned from the CIA after showing classified material to his mistress and biographer Paula Broadwell.

In 2015, he pleaded guilty to a misdemeanor charge of mishandling classified materials, and was put on two years' probation and fined US$100,000.

The scandal could pose a problem for getting Senate approval and would expose Trump to accusations of hypocrisy after he savaged Hillary Clinton on the campaign trail for mishandling classified emails as secretary of state.

On Tuesday, Trump fleshed out his cabinet by nominating a fierce Obamacare critic as health secretary - Congressman and former surgeon Tom Price, indicating that he plans to tear up the divisive healthcare law.

FOX IN HEN HOUSE

Price "is exceptionally qualified to shepherd our commitment to repeal and replace Obamacare," Trump said as Democrats criticized the nomination.

Incoming Senate Minority Leader Charles Schumer called it "akin to asking the fox to guard the hen house."

The president-elect has also selected Elaine Chao, the Taiwan-born former labour secretary as transportation secretary, US media reported.

In between back-to-back job interviews, Trump has continued to fan alarm and inflame critics by indulging in his customary tweet storms.

On Tuesday he sparked uproar by saying nobody should be allowed to burn the US flag - allowed under the US constitution that safeguards freedom of expression - and that it should be punished by loss of citizenship or one year in jail.

And he embarked on a Twitter rant against CNN, complaining about their coverage and retweeting posts insisting that voter fraud did take place on Election Day.

Experts and officials across the political spectrum disparaged his unsubstantiated claim that "millions" of Americans voted illegally.

The Republican billionaire won the Electoral College 306 to 232 for Clinton, although the Democrat won the popular vote by more than two million ballots.

Observers deny any evidence of widespread fraud and say potential recounts in Wisconsin, Pennsylvania and Michigan will not change the outcome.