During the campaign, many of Donald Trump's supporters and even his advisers said they took many of the candidate's most far-reaching promises seriously but not literally.

Now in his first week at the White House, President Trump is showing that at least some of them were indeed meant literally - putting him at odds not only with critics but with some members of his own party.

The Trump Administration is showing every sign of taking the US far to the right in an effort to make good on a number of his pledges, including barring refugees and immigrants from some Muslim-majority countries, potentially implementing an ideological test for others, working to build a wall on the border with Mexico and even exploring the possibility of reopening a caustic debate over "enhanced interrogation techniques" such as waterboarding.

"He's never taken a position that he doesn't agree with. He's never taken a position that he doesn't believe in," said Sam Nunberg, a former Trump adviser.

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"The idea that he wasn't going to be a results-oriented president on the platform he ran on, that he designed, was a complete misnomer."

The White House said that no one should be surprised that Trump is trying to follow through on his campaign promises, starting with bold, if controversial, executive actions.

"The biggest thing is the President is somebody who likes to get things done," said Sarah Huckabee Sanders, the principal deputy White House press secretary.

"He's very much an executive. He's a builder. He likes to map out a plan and see it all come to fruition. He mapped out a plan to win the presidency, he won, and now he's implementing the policies he campaigned on. He's not somebody who sits back and waits for things to happen."

With an executive action today, Trump signalled he would start with one of the biggest: the process of constructing the wall with Mexico.

At the same time, in attempting to fulfill that promise, Trump is illustrating the limits of his approach. His vow to make Mexico pay for the wall remains unfulfilled, and he has not detailed any new plans to accomplish it.

"We do not need new laws," Trump said, a tacit acknowledgment that Congress had not yet signed on to the proposal. "We will work within the existing system and framework."

Some congressional Republicans, including Senator John McCain, have already reacted with alarm at reports that Trump could seek to reopen CIA "black sites" and revisit banned "enhanced interrogation techniques" that he advocated during the campaign.

The position would also put Trump at odds with his Defence Secretary, retired General James Mattis, who Trump said last year had lobbied him strenuously in opposition to the interrogation practices.

But Trump appears to be determined to press the issue, telling ABC News in an interview that he "absolutely" believes that waterboarding works.

Some of his initial executive actions have been more symbol than substance.

An executive order aimed at muzzling regulations associated with the Affordable Care Act signed by Trump on Inauguration Day is all but moot until Trump's Cabinet secretaries are confirmed by the Senate and in their jobs.

And his announcement on Tuesday of a withdrawal from the Trans-Pacific Partnership was simply the final and expected end for the 12-nation trade deal, which had languished in Congress.

Trump also promised today to stop "sanctuary cities" that decline to help enforce federal immigration laws, but his executive order simply instructs his homeland security secretary to withhold some federal grants from such jurisdictions.

The Trump Administration made a show of putting the measures into place, with signing ceremonies staged in the Oval Office and Trump's visit to the Department of Homeland Security.

Trump also moved quickly on other items that have long been on the Republican Party's wish list, beginning with authorizing federal agencies to ease the regulatory burden of the Affordable Care Act, banning federal funds for non-governmental organisations that provide or counsel women on abortions, and reauthorising construction on two controversial oil pipelines.

"He is the new action hero for America," said Republican Congressman Mike Kelly, who declared himself "very pleased" about Trump's first five days.

Kelly said he was particularly happy about Trump's efforts to clear the way for the construction of the Keystone XL and Dakota Access pipelines. "People kind of sit back and say, 'I can't believe he did it that quickly.' And other people say, 'I can't believe it took that long.' How many more studies do we have to do?"

But some Republicans said that while Trump is making good on his broad campaign promises, he has undermined his success through his inability to focus on a core message, instead allowing himself to succumb to petty distractions.

This week, Trump hosted jobs-focused meetings with auto and other business executives and union leaders and arranged for the groups to hold news conferences outside the West Wing to debrief the media, an opportunity to amplify a message about job creation.

But news has been dominated by Trump's fixation with the crowd size at his inauguration, his press secretary's airing of grievances against the media and Trump's unsubstantiated insistence to congressional leaders that millions of illegal votes had been cast in November, costing him the popular vote.

"I thought a lot of what's happened has actually been good - the meetings with automobile makers, unions and everything else," said Republican Congressman Adam Kinzinger. "When you argue over crowd size, when you argue over, you know, voter fraud, things like that, you're taking your eye off the message and, I think, harming your ability to unify Republicans in the country."

Trump's moves have alarmed Democrats, some of whom were cautiously optimistic that they could work with Trump as a self-proclaimed non-ideological dealmaker but who now see him fulfilling their worst fears.

"During the campaign, the president ran against both the Democratic and Republican establishments," said Democrat Senator Charles Schumer. "But since he was elected he has governed entirely from the hard right, totally ignoring all of the promises he made to working people during the campaign."

Trump's week of executive orders, codifying his most contentious campaign positions, has also signalled to Democrats that he does not intent to moderate on much as president.

"I'm particularly concerned with his penchant for pronouncements, his being challenged on those pronouncement and his doubling down and tripling down on them," said Democrat Congressman Adam Schiff, ranking Democrat on the House Intelligence Committee. "I had very low expectations for what a Trump presidency would be, but he's proven far worse than I expected."