(CNN) Donald Trump has made one thing clear, there's a strong man now in the Oval Office.

But while the emerging Trump doctrine is based on uncompromising presidential strength, the foreign policies that will define his administration are much less clear. US allies and enemies still don't know whether the new White House simply represents a change of tone or a true shift in America's global role.

Since taking office two weeks ago, the new President has shown little patience for diplomatic subtlety.

He dealt brusquely with allies like Mexico and Australia, expressed hostility to the European Union, defended Russian President Vladimir Putin and put Iran "on notice." His conduct has exacerbated global concerns about a President who campaigned on a populist platform deeply critical of the existing world order and questioned the value of US alliances.

And while the administration denies that restrictions on travel from seven countries represent a "Muslim ban" administration officials do not dispute that Trump has dispensed with what he sees as a politically correct view of Islamic radicalism pursued by two administrations since 9/11.

Trump's self-styling as a brawny leader will continue when he travels to MacDill Air Force Base in Tampa, the headquarters of Central Command and Special Operations Command on Monday to meet generals and address troops.

The visit follows a US raid on an Al-Qaeda camp in Yemen in which a Navy SEAL was killed, acting on Trump's first operational order as President.

CENTCOM has responsibility for the Gulf Region that includes Iran, so Trump's visit will be seen as no coincidence amid escalating tensions with Tehran triggered by its test firing of a ballistic missile just over a week ago, a development seen as laying down an early gauntlet to the new president.

"They are not behaving themselves," Trump told reporters Friday after a week of swiftly rising tensions with Tehran.

But it is not yet clear whether Trump's dominant, theatrical presidential persona is more an attempt to keep faith with voters who elected him, or part of a deeply conceived new foreign policy strategy.

"From now on, it's going to be America First. That's how I got elected, that's why you voted for me, and I will never forget it," Trump said in his weekly weekend address. Those comments gave credence to theories that Trump's tough guy swagger is more of a political device than a thought out diplomatic gambit. And his administration's first serious attempts to engage the world are provoking questions about exactly who is the dominant voice in foreign policy.

Mattis, Haley differ from Trump statements

After a campaign in which Trump cast doubt on US alliances in Asia, his new defense secretary, James Mattis, used his first trip to the region to reassert conventional US security guarantees to Japan and South Korea.

He also said he didn't see any need for "dramatic military moves" in the South China Sea, contradicting earlier White House suggestions that Washington would move aggressively to counter Beijing's territorial claims in the region.

Trump's ambassador to the United Nations, Nikki Haley, added to the uncertainty when she said last week sanctions would remain on Russia until it left Crimea. Her stance -- in line with the previous administration's policy -- appeared to conflict with Trump's desire to improve relations with Moscow.

Combined with last week's confirmation of Secretary of State Rex Tillerson, the White House's control of foreign policy over the past two weeks may also start to be counterbalanced by other institutional influences in Washington.

Embracing Putin

Trump added to the confusion on foreign policy on Sunday when he appeared to draw a moral equivalence between Putin, who has been accused of murdering journalists and political opponents, and the United States.

"There are a lot of killers. You think our country's so innocent?" Trump asked Fox News anchor Bill O'Reilly in a Super Bowl half time interview.

The tension between Trump's strongman instincts and more mainstream foreign policy influences in his team are one reason why leaders such as British Prime Minister Theresa May and Japanese Prime Minister Shinzo Abe (who will be in Washington this week) were so keen to meet him early on.

"This administration has a great difficulty in concluding any type of policies because of the tremendous ideological contradictions that exist within the administration itself," Trita Parsi, President of the National Iranian American Council told CNN on Saturday.

"Part of the reason why we are seeing this chaos is precisely because (of) a few people inside the White House and the (National Security Council) trying to run over the entire bureaucracies."

Aimed at a domestic audience

Many of Trump's first moves in foreign policy appear to have been rooted as much in domestic politics as global strategy, for instance his executive order on the travel bans, his telephone showdown with Australian Prime Minister Malcolm Turnbull over a refugee deal and a feud with Mexico over its refusal to pay for a border wall that led to the cancellation of a presidential visit.

But those political machinations are causing confusion around the world.

"My general reaction is that it has been fairly chaotic," said former Democratic Secretary of State Madeleine Albright on "Fareed Zakaria GPS" Sunday.

Critics of Trump's brazen approach worry that the president's penchant for personalizing disputes risks laying down red lines, alienating allies and sending conflicts spinning out of control.

New Iran plan

Nowhere is the new strutting tone of US diplomacy more obvious than in the case of Iran.

The new White House leapt at a chance to show its toughness, sending a signal that it intends to confront Tehran's efforts to project power in the region in a way that threatens US allies, for instance complaining at attacks on Saudi ships by Iranian backed Houthi rebels fighting a civil war in Yemen.

In a striking signal of a new US approach, Trump sent National Security Adviser Michael Flynn into the White House briefing room to warn on Wednesday that Iran was now "on notice."

The new administration believes that former President Barack Obama downplayed Iran's activity in the wider Middle East, including support for terrorism to safeguard his legacy-enhancing nuclear deal.

"Iran is playing with fire, they don't appreciate how 'kind' President Obama was to them. Not me!" Trump wrote on Twitter on Friday.

But there is little clarity on how far the administration will go to confront Iran. Officials say that sanctions imposed on Friday do not mean that Trump will follow through on campaign trail threats to trash the nuclear deal.

The tough rhetoric though has some analysts worried that the new administration could be starting an escalation it can't control.

"They are going to test again, then the question is what does the administration do? " said Aaron David Miller, a former US Middle East negotiator for Republican and Democratic administrations.

"They have begun to draw a line and if you don't respond in a tougher way then you are perceived to be weak or are humiliated. If in fact you respond militarily you create an escalatory cycle."

Trump spokesman Sean Spicer says the air of uncertainty is deliberate and is part of a campaign to keep other leaders guessing.

"I think one of the things that the president has said throughout the campaign, during the transition and since becoming president, is that he doesn't like to telegraph his options," Spicer said.

"That's how he believes that you can have a much greater successful option."

James Jay Carafano, a Heritage Foundation analyst who worked on Trump's transition team believes that seeking deep foreign policy truths in the President's tweets and comments is a mistake.

"That public persona is not strategic signaling. That is just Trump being Trump. Pretty soon, people are going to look for other things when they look at what is true strategic signaling," Carafano said.

"Trump means exactly what he says, you just have to figure out exactly what he means," Carafano said.