President Donald Trump's spats with US allies as close as Mexico and as unlikely as Australia are leaving his new secretary of state and others in his Cabinet to clean up a lot of potential damage.

It's a good-cop, bad-cop dynamic that could define America's foreign policy for the next four years.

Trump's first two weeks on the job have rattled foreign friends and foes alike and even members of his own party starting with his order to temporarily halt all refugee admissions as well as immigration from seven mainly-Muslim countries.

Concern only escalated the past few days with his personal dust-ups with foreign leaders and declaration that Iran is now “on notice” for possible American action.

“It's time we're going to be a little tough, folks,” Trump said at a National Prayer Breakfast on Thursday, as unseemly details circulated about his private phone calls with the Mexican and Australian leaders.

“We're taken advantage of by every nation in the world virtually. It's not going to happen anymore,” he added.

Trump's blunt comments came a day after word emerged of a tense discussion with Australian Prime Minister Malcom Turnbull, in which the new US president lambasted an Obama-era deal to resettle some 1,600 asylum-seekers.

Diplomatic dysfunction was clear. Minutes after the US Embassy in Canberra said the deal was still on, Trump seemed to contradict that message, tweeting: “I will study this dumb deal!” On the other side of the globe, new details emerged about strained ties between the US and its southern neighbour.

There was already irritation on both sides following Mexican President Enrique Pena Nieto's cancellation of a trip to Washington after Trump made the visit contingent on Mexico agreeing to pay for a US border wall.

In a follow-up phone call, Trump warned Pena Nieto that he was ready to send US troops to stop “bad hombres down there” if Mexico's military can't control them, The Associated Press learned.

The White House said the comments were made in a “lighthearted” manner. But administration officials described the calls with both leaders as contentious.

Some top aides are underscoring Trump's emphasis on toughness and brawnier US negotiations, dominant themes of his “America First” foreign policy.

At the United Nations, Trump's U.N. ambassador, Nikki Haley, said the US would be “taking names” of countries that “don't have our back.”

His national security adviser, Michael Flynn, made a surprising appearance at the White House daily briefing to “officially” put Iran “on notice” after its ballistic missile test.

Trump topped Flynn Thursday by saying “nothing is off the table” when it comes to a potential American response.

But Trump's top diplomats are striking noticeably softer tones.

Rex Tillerson, in his first day as secretary of state, implicitly acknowledged in an address to staff that many US diplomats oppose some of Trump's positions. Without criticising that, he called for unity.

“Honesty will under-gird our foreign policy, and we'll start by making it the basis of how we interact with each other,” Tillerson said. “We are human beings first.”

The former Exxon Mobil CEO offered an olive branch to hundreds of diplomats who signed a “dissent cable” challenging Trump's order on immigration and refugees, affirming that “each of us is entitled to the expression of our political beliefs.”

While noting the nation's “hotly contested” election campaign, Tillerson stressed that “we cannot let our personal convictions overwhelm our ability to work as one team.”

Defense Secretary Jim Mattis sought to project the same sentiment internationally in South Korea on Thursday, in his first official trip abroad.

He said the president's message was “about the priority that we place on this alliance between our two nations,” seeking to reassure an ally that was unnerved by Trump the candidate when he said it should take on greater self-defence responsibility.

While Trump drives foreign policy from the White House, he appears to be tasking his top Cabinet officials with the responsibility of follow-up reassurance.

They're also fielding questions from allies about his taboo-shattering language and trying to clarify the true US positions behind the rhetoric.

Though Tillerson himself lacks experience as a diplomat, he portrayed himself in his Senate confirmation hearing as a level-headed tactician with foreign policy views within the Republican mainstream.

He spent his first day at work meeting with Jordan's King Abdullah II and German Foreign Minister Sigmar Gabriel.

For many of Trump's supporters, each new antagonistic tweet, statement or executive order has been a fresh measure of proof that he intends to shake up a foreign policy establishment they reject and fulfil his promise to put “America first.”

They argue he is reasserting American strength after the weakness of the Obama administration.

After winning the presidency, Trump quickly ruffled China, a chief American economic and political rival, with a call to the president of Taiwan, breaking longstanding US policy.

Trump's first meeting with a foreign leader, last week with British Prime Minister Theresa May, had been a bright spot in his diplomatic debut.

But his immigration order brought thousands of protesters to London's streets labelling her “Theresa the Appeaser.”

Foreign Secretary Boris Johnson then called Trump's order “divisive, discriminatory and wrong.” Trump's warnings to Iran prompted a more hostile response from Tehran on Thursday.

“It is not for the first time that a naive person from the U.S. poses threats to Iran,” said Ali-Akbar Velayati, foreign adviser to Ayatollah Ali Khamenei, Iran's supreme leader.

According to Iran's state-run IRNA news agency, Velayati said: “The US will be the final loser.”

Meanwhile, it fell to Sen John McCain, a hawkish Republican, to smooth relations with Australia.

McCain said he phoned Australia's ambassador to affirm “unwavering support for the US-Australia alliance.”