Donald Trump vowed a new "golden age" as he took the oath for a historic second US presidential term on Monday, painting a picture of an America in decline that only his hardline policies can restore to glory.

In an address in the US Capitol, the 47th president promised a blitz of orders including the declaration of a national emergency on the Mexican border and a policy of only recognizing two genders.

Trump also struck a nationalistic tone as he capped the most extraordinary comeback in US political history, pledging to impose trade tariffs, rename the Gulf of Mexico the Gulf of America, and take "back" the Panama Canal, which has been controlled by the Central American country since 1999.

"The golden age of America begins right now. From this day forward our country will flourish and be respected again all over the world," Trump said in the Capitol, where the inauguration was held indoors for the first time in decades, due to freezing weather.

The Republican even appeared to suggest he was on a divine mission, saying "I was saved by God to make America great again" after escaping an assassin's bullet at an election rally in July.

While promising renewal, Trump denounced what he said had been a "betrayal" of Americans by a "radical and corrupt establishment" under outgoing President Joe Biden.

"America's decline is over," said Trump, who at 78 is now the oldest president ever to take office.

Biden, 82, who had earlier hosted Trump and his wife Melania at the White House for tea, watched on as his political rival read the last rites over his single term in office.

Biden's last acts in office included preemptive pardons of former officials and his own siblings to shield them from Trump.

Russian President Vladimir Putin congratulated Trump and said on Monday he was open to talks on the Ukraine conflict. (AFP)