Donald Trump on Monday (AEDT) recast himself as a more moderate US president in waiting, expressing flexibility on his core campaign pledges to build a wall on the Mexico border, deport illegal immigrants, prosecute Hillary Clinton and axe President Obama’s healthcare law.

“I’m a very sober person,” the president-elect said.

In his first television interview since being elected, Mr Trump also committed to making “major tax reform” such as corporate cuts a priority, an economic policy shake-up that has helped spur financial markets over the past week.

US share index futures rose modestly around the time of his remarks, on 60 Minutes, ahead of Monday’s market opening on Wall Street.

Adding to signs that Mr Trump has moderated from the brash outspoken candidate, he named Republican establishment figure Reince Priebus as the powerful White House chief of staff.

The appointment buoyed hopes Mr Trump was preparing to govern seriously and broker deals with Congress to legislate changes to tax, immigration and healthcare.

However, sending a conflicting signal, Mr Trump named arch-conservative Stephen Bannon as his chief strategist and senior counsellor.

Mr Bannon operates the populist conservative Breitbart News Network website that channels white, nationalist rhetoric.

On shutting out illegal immigrants on the Mexico border, Mr Trump said he was open to building a fence, rather than a wall, on sections of the border.

Rather than deporting up to 11 million illegal immigrants, Mr Trump watered down the pledge to focus immediately on the 2-3 million convicted criminals, drug dealers and gang members who did not have visas to live in the US.

After securing the border, Mr Trump said he would then make a “determination” on the other “terrific people” living illegally in the US.

After meeting Barack Obama at the Oval Office last week, Mr Trump said he would like to retain elements of the Democratic President’s healthcare insurance law, including non-discrimination against pre-existing conditions and adult children being on the plan of their parents.

He said he would repeal and replace Obamacare with a system that would deliver better healthcare at a cheaper cost.

Mr Trump, a former celebrity TV star, was also ambivalent about his campaign pledge to appoint a special prosecutor to review Mrs Clinton’s government emails and the Clinton Foundation’s potential conflicts of interest.

He said the Democratic nominee did some “bad things” and he would “think about it”, but would prioritise jobs, healthcare, border security and immigration.

Amid protests in more than 10 cities in response to his improbable victory and attacks by some of his supporters on Muslims, Hispanics and gays, Mr Trump urged them to “stop it” and said minorities fearful of him should not to be afraid.

“I’m going to bring this country together,” he said.

He later blamed professional protesters, media inflammation and “double standards” for the demonstrations against him.

Still, there were shades of the controversial candidate who offended about half of America with his attacks on Muslims, Mexicans and prominent women during his vicious 16 month campaign.

He planned to keep tweeting to his 28 million followers as president, saying it was a “great form of communication” to “get the word out”.

He reiterated that parts of the election system were “rigged”, even though at least one million people more voted for Mrs Clinton but she lost the electoral college to Mr Trump.

The president-elect vowed to “knock out” the Islamic State terrorist group, but refused to outline how and again claimed he probably knew more than military generals.

He would not comment on whether he would ask FBI director James Comey to resign, after his contentious on-again, off-again probes into Mrs Clinton’s emails before election day.

Earlier, the president-elect said he received a “lovely call” from Mrs Clinton last week congratulating him on winning the presidency, saying “she couldn’t have been nicer”.

Former president Bill Clinton also telephoned him and was “very nice”, he said.

After a nasty campaign where Mr Trump called Mrs Clinton “corrupt” and “crooked Hillary”, the former celebrity TV star said he did not regret his conduct and was “very proud” of winning.