US president-elect Donald Trump picked Reince Priebus, the Republican National Committee chairman, as the White House chief of staff, and Steve Bannon of Breitbart News as chief strategist and senior counselor.

These were Trump's first important staffing decisions. The chief of staff is the highest-ranking employee in the White House.

"I am thrilled to have my very successful team continue with me in leading our country," Trump said in a statement on Sunday. "Steve and Reince are highly qualified leaders who worked well together on our campaign and led us to a historic victory."

"Now I will have them both with me in the White House as we work to make America great again."

Priebus said: "I am very grateful to the president-elect for this opportunity to serve him and this nation as we work to create an economy that works for everyone, secure our borders, repeal and replace Obamacare and destroy radical Islamic terrorism."

In an interview with CBS News, Trump said his administration will move immediately to deport or incarcerate millions of undocumented immigrants who have criminal records.

The president-elect estimated there are "probably 2 million, it could even be 3 million" gang members, drug dealers and other people with criminal records who are illegally in the country, according to excerpts of the interview released earlier Sunday.

"We are getting them out of our country or we are going to incarcerate them," he told CBS less than a week after winning the US presidential election. The full interview will be broadcast later Sunday.

Trump said after those people are out of the country and the border is secure, his administration will make a determination on the status of the remaining millions of undocumented immigrants in the country, who he said are "terrific people."

The president-elect also said he would keep his promise to build a wall along the US border with Mexico, but said part of it could be a fence, as some members of Congress have suggested.

"There could be some fencing," he said in the interview, but in other areas "a wall is more appropriate."

Trump said he would make "very restrained" use of social media as head of state, after relying on Twitter heavily during the campaign to voice his opinion.

The comments came as the president-elect tweeted several times on Sunday complaining to the New York Times about the "highly inaccurate coverage of the 'Trump phenomena'."

His criticism made note of a letter from New York Times publisher Arthur O Sulzberger Jr pledging to subscribers that the newspaper would "report America and the world honestly, without fear or favour" as Trump takes office.

The president-elect tweeted that the paper "sent a letter to their subscribers apologizing for their BAD coverage of me."

Trump called Twitter "a great form of communication," in particular as a means of fighting negative coverage from the media, which he often accuses of being biased.

"When you [the press] give me a bad story ... I have a method of fighting back," Trump told CBS.

Trump was known throughout the campaign for his aggressive and spontaneous late-night tweets.

"I'm not saying I love it, but it does get the word out," Trump said.