Donald Trump became the 45th president of United States on Friday, and placed the battle against "radical Islamic terrorism" at the heart of his foreign policy, vowing to work with allies to destroy the militant threat.

“We will reinforce old alliances and form new ones and unite the civilised world against radical Islamic terrorism, which we will eradicate completely from the face of the earth,” he declared.

The 70-year-old Republican billionaire placed his left hand on a bible used by Abraham Lincoln and recited the 35-word oath spoken since George Washington, and then launched into a much-anticipated inaugural address.

“We, the citizens of America, are now joined in a great national effort to rebuild our country and restore its promise for all of our people,”

Trump told a crowd of hundreds of thousands massed on the National Mall.

“Together we will determine the course of America, and the world, for many, many years to come,” he said.

“From this day forward, it's going to be only America first.”

Trump's inauguration caps the improbable rise to power of the Manhattan real estate mogul, who had never before held elected office, served in the government or the armed forces.

A crowd of hundreds of thousands looked on, including outgoing president Barack Obama and Trump's defeated election opponent Hillary Clinton - who narrowly missed out on becoming America's first female president.

Meteoric political rise

When Trump descended the escalators of his glitzy New York tower in June 2015, his run for office was dismissed and even mocked.

His staff, many shunned by friends for supporting a man who has been labeled a racist and bigot by his critics, will become power players in the White House.

In the primaries, Trump dominated a crowded Republican presidential field with smash-mouth rhetoric and star power. He rode that same wave of anti-elite sentiment to victory over Clinton in the November election.

For Trump's critics, there was disbelief that a man who 19 months ago hosted “The Apprentice” is now leader of the free world.

Time-honoured traditions

At 70 years of age, Trump is the oldest man ever to begin work in the Oval Office.

He has vowed to tear up Obama's policies and re-examine decades-old alliances with Europe and in Asia. Beginning Friday, his team plans a rolling series of daily executive orders to roll back Obama's agenda.

His inauguration was notably more sparsely attended than that of Obama in 2009 and 2013.

Many will look to Trump's inaugural speech for efforts to unify a country divided by politics - and increasingly, by culture.

The most noted inaugural addresses had sought to lift Americans' gaze up from the rancor and troubles of the day toward the horizon and a better tomorrow.

Inaugural addresses - from Lincoln to John F. Kennedy - echo across American history. Phrases like “malice towards none” and “ask not what your country can do for you” have been carved into the vernacular.

Trump aides promised an address that is at once short - at around 20 minutes - and philosophical.

Earlier in the day, Trump had traced the steps of many presidents past, attending a prayer service at St. John's Church before heading to the White House, where he was greeted warmly by Obama.

“Mr President-elect, how are you?” Obama asked his successor, after having deposited a letter in the Resolute desk and left the Oval Office for the last time.

After his speech, Trump will attend a luncheon inside the Capitol, before heading back to the White House to begin the business of governing.

Vandalism erupts at anti-Trump protest

Police fired gas to disperse protesters after stones were thrown and windows broken in Washington on Friday ahead of Donald Trump's presidential inauguration.

As Trump, his supporters, former presidents and other dignitaries gathered on the National Mall for the swearing-in ceremony, opponents marched in nearby streets and were confronted by a heavy police presence.

Most of the noisy protests - including those by an array of anti-racist, feminist, pro-immigration, anti-war and marijuana legalisation groups - were peaceful.

But in at least one incident, black clad youths emerged from the crowds to smash windows in a bank and fast food outlet and throw stones, as riot police deployed pepper spray.

Marchers chanted: “No deportation, no KKK, no fascist USA!” A 27-year-old financial worker from Tampa Bay in Florida, who did not want to give his name for fear of retaliation by his employer, said Trump's election victory had left him fearful.

“There is nothing to hope for except for grassroots efforts to oppose him,” he told AFP.

Public interest lawyer Renee Steinhagen, 61, came down from New York to protest against Trump's inauguration.

“I'm doing this to express resistance to the change that await us,” she said.

“This administration seems more extreme than any other. This is a simple act of resistance. It's better than staying at home.”

A few blocks away, Trump's supporters chanted “USA! USA! USA!” as the president-elect arrived at the Capitol to be sworn in as the 45th US president.