Former New York Mayor Rudy Giuliani has emerged as the favorite to be secretary of state in Donald Trump's administration, a senior Trump official said on Monday night, according to The Telegraph.

The official told The Associated Press that there's no real competition for the job and that it's the former New York mayor's if he wants it. The official wasn't authorized to speak on the record and requested anonymity.

While speaking at a Wall Street Journal CEO Council event on Monday night in Washington, the former mayor and federal prosecutor said he wouldn't be attorney general in a Trump administration. He had been considered a leading prospect for that job even before Mr Trump's victory last on Tuesday.

The position of secretary of state arose during the event, but Mr Giuliani appeared to be coy about his own prospects. He said John Bolton, the former ambassador to the United Nations, would be a very good choice. Asked if there was anyone better, he replied: "Maybe me, I don't know."

As he formed his administration, the president-elect was considering whether to inject new diversity into the GOP by recommending a woman to lead the Republican Party and an openly gay man to represent the United States at the United Nations.

The moves, among dozens under consideration from his transition team, follow an intense and extended backlash from Mr Trump's decision on Sunday to appoint Steve Bannon, a man celebrated by the white nationalist movement, to serve as his chief strategist and senior adviser.

"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," said House Democratic leader Nancy Pelosi. She called Mr Bannon's appointment "an alarming signal" that Mr Trump "remains committed to the hateful and divisive vision that defined his campaign."

His inauguration just 66 days away, however, Mr Trump focused on building his team and speaking to foreign leaders. He remained 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 in a readout that "he is very much looking forward to having a strong and enduring relationship with Russia and the people of Russia." Mr Trump has spoken in recent days with the leaders of China, Mexico, South Korea and Canada.

At the same time, Mr Trump was 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. Mr Grenell, known in part for aggressive criticism of rivals on Twitter, previously served as US spokesman at the UN under president George W Bush.

Mr Trump was also weighing whether to select Michigan GOP chairwoman Ronna Romney McDaniel, a niece of chief Trump critic and 2012 presidential nominee Mitt Romney. She would be the second woman ever to lead the Republican National Committee - and the first in four decades.

Appointing Mrs McDaniel to run the GOP's political arm 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.

The personnel moves under consideration were confirmed by people with direct knowledge of Mr Trump's thinking who were not authorized to publicly disclose private discussions. They stressed that the decisions were not final.

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, who led a website that appealed 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 on Monday 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.

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."

The outgoing president encouraged Mr Trump, however, to embrace a unifying tone.

Mr Trump's hires were, at first glance, contradictory, though they fit a pattern of the celebrity businessman creating a veritable Rorschach test that allowed his supporters to see what they wanted. Mr Priebus, who lashed the RNC to Mr Trump this summer despite some intraparty objections, is a GOP operative with deep expertise of the Washington establishment that the businessman has vowed to shake up. He has close ties to house speaker Paul Ryan, a fellow Wisconsinite.

Mr Bannon, meanwhile, helped transform the Breitbart News site into the leading mouthpiece of the party's anti-establishment wing, which helped fuel the businessman's political rise. Mr Ryan has been one of his most frequent targets.

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

Mr Bannon, Mr Greenblatt said, "presided over the rise of Breitbart as a haven online" for the "alt-right." 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."