A billionaire Saudi prince has congratulated US president-elect Donald Trump after previously calling him a disgrace who should have pulled out of the race.

"President elect @realDonaldTrump whatever the past differences, America has spoken, congratulations & best wishes for your presidency," Prince Alwaleed bin Talal said on his official Twitter account, after US election results on Wednesday confirmed Trump's unexpected victory over Hillary Clinton.

Alwaleed is an unusually outspoken member of the Saudi royal family who chairs Kingdom Holding Co. The diversified firm's interests include US-based giants Citigroup and Time Warner.

Late last year Alwaleed took exception to what his office called Trump's "anti-Islam statement", a proposal that all Muslims should be temporarily barred from entering the United States.

"You are a disgrace not only to the GOP but to all America," Alwaleed tweeted to Trump, referring to the Republican Party.

"Withdraw from the US presidential race as you will never win."

Trump hit back, also on Twitter.

"Dopey Prince Alwaleed Talal wants to control our US politicians with daddy's money. Can't do it when I get elected," he wrote at the time.

Trump later modified his stance on Muslims to urge an immigration ban from countries with "a proven history of terrorism" and for "extreme vetting" of immigrants.