Trump and Melania dance at the ball [Photo: Courtesy]

Trump and Melania shuffled from side to side to a version of Frank Sinatra's classic before the 70-year-old burst into song

Donald Trump sang "I did it my way" as he shared an awkward first dance with his wife Melania at the first of two presidential inaugural balls last night.

And as Melania grinned nervously at the audience, Trump suddenly began singing along to the lyrics.

It was apt moment at the end a surreal day when the 70-year-old billionaire businessman and former reality TV star became the 45th President of the United States.

It was the first of two official Presidential Inaugural Balls, both at the Walter E. Washington Convention Center.

Both were held in the same building at the same time, but on different floors.

There were special appearances by Sam Moore, Tim Rushlow and his Big Band, Silhouettes, The Rockettes, Pelican212, The Piano Guys, Circus 1903, Cache Olson, Lexi Walker, and Erin Boheme.

The balls were open to the public but required a ticket to get in.

President Trump will also attend a third ball - the Salute to Our Armed Services Ball at the National Building Museum.

Earlier, President Trump was quick to assume the mantle of the White House, making his first executive order one aiming to axe his Barack Obama's signature healthcare law.

Hours after delivering a nationalistic speech during his swearing-in ceremony, Mr Trump sat at the president's formal desk in the Oval Office as he signed the order.

White House chief of staff Reince Priebus said it was aimed at "minimising the economic burden" of the "Obamacare" law.

The order notes that Mr Trump intends to seek the "prompt repeal" of the law.

But in the meantime, it allows the Health and Human Services Department and other federal agencies to delay implementing any piece of the law that might impose a "fiscal burden" on states, health care providers, families or individuals.

Moments later, Vice President Mike Pence administered the oath of office to Defence Secretary James Mattis and Homeland Security Secretary John Kelly, the first members of Mr Trump's Cabinet to clear Senate confirmation.