WASHINGTON -  Donald Trump, speaking after being sworn in as the 45th president of the United States on Friday, pledged to wipe out “radical Islamic terrorism" from the world, placing the war against militants on top of his foreign policy agenda.

Violent protests erupted in downtown Washington, just a mile from the spot where Donald Trump took oath of his office. Police moved in large groups to disperse mobs of demonstrators as tear gas lingered in the air and the pavement was speckled with broken glass.

Peaceful protesters milled around with signs like “not my president” "Say No to Islamophobia" and “say no to racism”, looking equally startled by the destruction. In addition to Starbucks the windows of a McDonald's, Wells Fargo bank and several cars had been smashed.

Just a short walk to the South, protesters had blocked security gates through which Trump’s supporters were to enter the inauguration.

Environmental activists, their arms linked, succeeded in keeping attendees out for an extended period of time before at last being forcibly removed.

Protesters blocked the entrance before the event, shouted abuse throughout and threw objects at attendees as they left.

In a 16-minute address at the domed US Capitol, he also vowed to put "America first" at all times and "protect our borders," but also vowed to strengthen old alliances and forge new ones.

“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,” Trump declared in a brief reference to international issues.

"We will seek friendship and goodwill with the nations of the world, but we do so with the understanding that it is the right of all nations to put their own interests first. We do not seek to impose our way of life on anyone, but rather to let it shine as an example."

As protests erupted elsewhere in Washington, Trump raised his right hand and put his left on a Bible used by Abraham Lincoln and repeated a 35-word oath of office from the US Constitution, with US Chief Justice John Roberts presiding.

Afterward, he hugged his wife, Melania, and other members of his family. Then he turned around to a podium and delivered his inaugural address.

"This moment is your moment, it belongs to you," Trump told a large crowd that had earlier booed Chuck Schumer, the Democratic minority leader in the US Senate.

Revisiting themes from his improbable campaign victory, Trump said his presidency would aim to help struggling middle-class families, build up the US military and strengthen US borders. "We are transferring power from Washington DC and giving it back to you," he said.

He promised a "great national effort" to rebuild the country for all its people, while lashing out at political opponents by saying that he would hand power he said is now held in Washington "back" to the people.

At home, he said he would "bring back jobs" he asserted had been "stolen" from the United States. “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 billionaire businessman, who had never before held elected office, served in the government or the armed forces.

Dignitaries including former President Bill Clinton and his wife Hillary Clinton, Trump's Democratic rival in the election, attended the ceremony on the steps of the domed Capitol building.

Members of the US Congress also attended but one-third of the Democrats in the US House of Representatives had said they would boycott the event.

Security was tight with thousands of law-enforcement officers deployed and kilometres of crowd barriers set up as about 900,000 people turned out in the capital for the inauguration, including thousands of protesters.

Most of the protests, including those by an array of anti-racist, feminist, pro-immigration, antiwar, and marijuana legalization groups concerned about statements Trump has made on those issues and others - were peaceful. Some marchers chanted: "No deportation, no KKK, no fascist USA!

Less than two hours before the swearing-in ceremony, TV footage showed black-clad activists charging down streets, overturning a garbage can, and smashing a plate-glass bank window. They also smashed a window at a fast-food outlet and threw stones, while police fired pepper spray.

Police in riot gear push the protesters off streets near the National Mall and said at least 95 were detained.

About 30 groups have obtained permits for protests they estimate will attract about 270,000 people on Friday and Saturday, far more than have been seen in other recent presidential inaugurations.

Earlier this week, a Washington Post-ABC News survey found Trump's 40 percent approval rating was the lowest of any incoming president-elect since Jimmy Carter in 1977.

Clashes also broke out between masked protesters and police in Washington, blocks away from the route of the parade about to start in honour of newly sworn-in President Trump.

Some 400 to 500 protesters hurled objects at police in riot gear, who responded with tear gas, in the second outburst of violence in the space of a few hours.

Washington police said they had arrested more than 90 people over acts of vandalism committed on the fringe of peaceful citywide demonstrations being held against Trump's inauguration.