US President-elect Donald Trump is considering whether to inject new diversity into the Republican party by selecting a woman to lead it and an openly gay man to represent America at the United Nations.

The moves, among dozens under consideration from his transition team, follow a backlash in the wake of Mr Trump's decision to appoint Breitbart News chief Steve Bannon, a man celebrated by the white nationalist movement, to serve as his chief strategist and senior adviser.

House Democratic leader Nancy Pelosi said: “After winning the presidency but losing the popular vote, President-elect Trump must try to bring Americans together - not continue to fan the flames of division and bigotry.”

She called Mr Bannon's appointment “an alarming signal” that Donald Trump “remains committed to the hateful and divisive vision that defined his campaign”.

With his inauguration just 66 days away, Mr Trump has focused on building his team and speaking to foreign leaders. He remains sequestered in Trump Tower in New York.

Inexperienced on the international stage, the Republican president-elect spoke to Russian president Vladimir Putin on the phone. His transition office said that “he is very much looking forward to having a strong and enduring relationship with Russia and the people of Russia”.

Mr Trump has also spoken in recent days with the leaders of China, Mexico, South Korea and Canada.

At the same time, Mr Trump is considering tapping Richard Grenell as US ambassador to the United Nations. He would be the first openly gay person to fill a Cabinet-level foreign policy post. Grenell, known in part for aggressive criticism of rivals on Twitter, previously served as US spokesman at the UN under former president George W Bush.

The president-elect is also weighing up whether to select Michigan's Republican chairwoman Ronna Romney McDaniel, a niece of chief Trump critic and 2012 presidential nominee Mitt Romney, as leader of the political arm of the party. She would be the second woman ever to lead the Republican National Committee, and the first in four decades.

“I'll be interested in whatever Mr Trump wants,” Ms McDaniel said.

Appointing Ms McDaniel could be an effort to help the party heal the anger after a campaign in which Mr Trump demeaned women. The appointment of Mr Grenell, who has openly supported same-sex marriage, could begin to ease concerns by the gay community about vice president-elect Mike Pence's opposition to same-sex marriage during his time as Indiana governor.

Internal deliberations about staffing come a day after Mr Trump made overtures to warring Republican circles by appointing Mr Bannon and RNC chairman Reince Priebus as his White House chief of staff.

The former media executive led Breitbart News, a conservative website that appeals to the so-called “alt-right” - a movement often associated with efforts on the far right to preserve “white identity,” oppose multiculturalism and defend “Western values”.

Mr Priebus defended the media mogul, saying the two made an effective pair as they steered Mr Trump past Democrat Hillary Clinton and toward the presidency. He sought to distance Mr Bannon from the incendiary headlines on his website, saying they were written by unspecified others.

Meanwhile, outgoing president Barack Obama avoided any direct criticism of Mr Trump's personnel moves during an afternoon news conference, suggesting that the new president deserves “room to staff up”.

“It's important for us to let him make his decisions,” Mr Obama said. “The American people will judge over the course of the next couple of years whether they like what they see.”

The outgoing president encouraged Mr Trump, however, to embrace a unifying tone, saying: “It's really important to try to send some signals of unity and to reach out to minority groups or women or others that were concerned about the tenor of the campaign.

“And I think that's something he will want to do.”

Jonathan Greenblatt, CEO and national director of the Anti-Defamation League, called Mr Bannon's selection “a sad day”.

Mr Greenblatt said that Mr Bannon “presided over the rise of Breitbart as a haven online” for the “alt-right”.

He said that the website under Mr Bannon's leadership “trafficked in the some of the worst tropes, not just only against Jews - but the anti-Semitism is real - but also against other minorities, particularly Mexicans and Muslims”.