US President-elect Donald Trump has made his first call to the leader of China, and is "getting his arms around our foreign policy" as he prepares to assume the leadership of the world's sole superpower, a top aide said Monday.

The Republican billionaire's diplomatic foray came as US President Barack Obama was about to leave for a farewell visit to Europe to reassure worried allies about a man he once warned was "unfit" to lead the United States.

Ensconced at his Trump Tower headquarters in Manhattan -- a magnet of street protests -- since his shock election on November 8, Trump and his inner circle were again working Monday to shape his new administration.

More cabinet-level appointments will be rolled out this week, Kellyanne Conway, Trump's campaign manager told reporters in New York.

His first two appointments came Sunday -- onetime Republican National Committee chair Reince Priebus is his White House chief of staff, and anti-establishment media firebrand Steve Bannon will be his chief strategist.

The appointment of Bannon -- the chief of ultra-conservative Breitbart News -- has raised hackles, with Jewish and Muslim leaders expressing concerns about Bannon, who has championed the so-called "alt-right" perspective.

The New York real estate mogul has also spent time calling world leaders, as he begins to develop ties with America's allies -- and adversaries.

Trump, who frequently savaged China on the campaign trail and threatened to impose a 45 percent tariff on Chinese-made goods, spoke with Chinese President Xi Jinping late Sunday.

He told Xi he believes they will have "one of the strongest relationships for both countries moving forward," the president-elect's transition team said early Monday.

They agreed to meet "at an early date" to discuss the relationship, Chinese state broadcaster CCTV said.

"Getting his arms around foreign policy" was one of Trump's four top priorities, along with health care, immigration and taxes, as he prepares for his first 100 days as president, said Priebus.

"I see president-elect Trump being very calm and cool and collected. And prepared to lead the American people," said Priebus, seen as an establishment counter-weight to Bannon, on ABC's "Good Morning America."

- 'Unbelievably interesting' -

Trump, a 70-year-old real estate developer and reality TV star who had never run for political office, has threatened to shake up America's most important international relationships.

In the campaign, he railed against free trade agreements, called NATO obsolete, suggested that Japan and South Korea get their own nuclear weapons, and spoke admiringly of Russia's President Vladimir Putin.

Last week, he met for 90 minutes with Obama at the White House -- an "unbelievably interesting" conversation about the "things that are tough right now," Trump told CBS's "60 Minutes" in an interview aired Sunday.

How much of Trump's agenda will survive the realities of governing remains an open question, but he has signalled that he intends to keep a populist edge by naming Bannon to his top team of advisors.

On the domestic front, Priebus said Trump's focus in the first 100 days would be on immigration, repealing and replacing Obama's health care reform, and legislation to cut taxes and simplify the tax code.

"Think we have an opportunity to do all of those things given the fact that we have the House and the Senate and we have an eager Congress ready to get work done," said Priebus.

Trump also will get to fill a vacant seat on the US Supreme Court as soon as he takes office, cementing a conservative majority that appeared to crack with the death of arch conservative Justice Antonin Scalia in February.

"The judges will be pro-life," Trump told CBS. "In terms of the whole gun situation, they're going to be very pro-Second Amendment," he added, referring to the constitutional right to bear arms.

Trump said as many as three million undocumented immigrants with criminal records -- "gang members, drug dealers" -- would be deported and incarcerated.

But he conceded that the famous wall he has vowed to build on the border with Mexican may be just a fence in places.

Told that many Americans are scared, Trump said: "Don't be afraid. We are going to bring our country back."

Obama was due to address reporters on Monday at about 3:15 pm (2015 GMT) -- perhaps offering his own reassurances to Americans and final thoughts on the election before heading abroad.

- 'Stop it' -

Trump said he was "saddened" by reports of harassment of Hispanics and Muslims, and told the perpetrators: "Stop it."

But huge street demonstrations have continued every night in New York and other cities since a surprise election in which Democratic nominee Hillary Clinton won the popular vote but lost the all-important electoral vote.

As he seeks to calm the turbulence, Trump has softened some stances and offered assurances on others -- indicating he would keep some aspects of Obamacare and would not seek to overturn the legalization of same-sex marriage.

He also confirmed he would forgo the $400,000 salary that comes with the office of US president.