Mitt Romney, former Republican presidential candidate and incoming US senator from Utah, sharply criticised President Donald Trump and said the US leader had caused dismay around the world.

In an opinion piece published in the Washington Post late on Tuesday, Romney criticised a number of Trump's actions in December.

"The appointment of senior persons of lesser experience, the abandonment of allies who fight beside us, and the president's thoughtless claim that America has long been a 'sucker' in world affairs all defined his presidency down," he wrote.

He added that "Trump's words and actions have caused dismay around the world."

Romney suggested that "on balance, (Trump's) conduct over the past two years ... is evidence that the president has not risen to the mantle of the office."

Trump hit back in an early morning tweet on Wednesday, saying, "Here we go with Mitt Romney, but so fast!"

Trump questioned whether Romney will be "a Flake", referring to outgoing Arizona Republican Senator Jeff Flake, who was a frequent critic of Trump.

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"Would much prefer that Mitt focus on Border Security and so many other things where he can be helpful," Trump said. "I won big, and he didn't. He should be happy for all Republicans. Be a TEAM player & WIN!"

Romney-Trump relationship

Romney's op-ed came as he and other politicians take up their seats in the new Congress. It is unclear whether Trump will face a serious challenge in 2020 in securing the Republican Party's presidential nomination.

Last February, Trump endorsed Romney's run for a Senate seat in Utah.

During the 2016 presidential campaign, Romney excoriated Trump as a "fraud" who was "playing the American public for suckers". Trump responded that Romney had "choked like a dog" in his unsuccessful 2012 campaign against Democratic President Barack Obama.

Despite Romney's prior criticism, after Trump won the presidency in November 2016, he briefly considered tapping Romney as secretary of state.

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In the op-ed on Tuesday, Romney said he "will speak out against significant statements or actions that are divisive, racist, sexist, anti-immigrant, dishonest or destructive to democratic institutions".

Romney has strongly defended press freedom and challenged Trump's repeated attacks on some news outlets as an "enemy of the people".

"The media is essential to our Republic, to our freedom, to the cause of freedom abroad, and to our national security. It is very much our friend," Romney wrote in an essay in November.