Updated 8.54pm

Donald Trump took power as the 45th president of the United States today and pledged to end the "American carnage" of social and economic woes in an inaugural address that was a populist and nationalist rallying cry.

Sketching a bleak vision of a country he said was ravaged by rusted-out factories, crime, gangs and drugs, Trump indirectly blamed his predecessors in the White House for policies that helped Washington at the expense of struggling families.

"From this moment on, it's going to be America First," the Republican told thousands of people gathered on the grounds of the National Mall as he took over the presidency from Democrat Barack Obama.

READ: Donald Trump's inauguration speech in full

Away from the ceremony, masked activists protesting against Trump ran through the streets smashing windows at a McDonald's restaurant, a Starbucks coffee shop and a steakhouse several blocks from the White House. They carried black anarchist flags and signs that said, "Join the resistance, fight back now."

Aerial pictures of the crowds of Trump supporters on the Mall showed a much smaller turnout at midday on Friday than that in comparable photos from Obama's first inauguration in 2009. Estimates of the crowd size were not immediately available from police.

In his short speech, Trump accused the Washington establishment of protecting itself but abandoning regular citizens who have suffered from poverty and crime.

"This American carnage stops right here and stops right now," he said. "Every decision on trade, on taxes, on immigration, on foreign affairs, will be made to benefit American workers and American families," he said.

Trump, 70, takes over a country divided after a savage election campaign.

The dark vision of America he often paints is belied by statistics showing low levels of unemployment and crime nationally, although Trump won many votes in parts of the nation where manufacturing industry has been badly hit.

A wealthy New York businessman and former reality TV star who has never held public office, Trump will set the country on a new, uncertain path at home and abroad.

WORLD REACTION

Trump's election was greeted with concern by many countries around the world, in part because of the potential for an isolationist foreign policy.

In an interview after Trump was sworn in, German Vice Chancellor Sigmar Gabriel said, "What we heard today were high nationalistic tones."

"I think we have to prepare for a rough ride," he told public broadcaster ZDF, adding Europe should stand together to defend its interests.

Mexican President Enrique Pena Nieto congratulated Trump on his inauguration, but cautioned that the sovereignty, national interest and protection of Mexicans would be paramount.

Mexicans have been angered by Trump's pledge to build a wall along the southern US border to keep illegal immigrants out, and to make Mexico pay for it. Trump has also frequently criticised US companies who have manufacturing operations in Mexico.

On financial markets, the dollar was down but US stock indexes pared their gains in the last day of a choppy trading week, after Trump's inaugural speech prompted investor concern about protectionist trade policies.

Pope Francis urged Trump to be guided by ethical values, saying he must take care of the poor and the outcast during his time in office.

In Moscow, Russians hoping Trump will usher in a new era of detente celebrated his inauguration. Russian nationalists held an all-night party at what used to be the main Soviet-era post office in Moscow. East of there, in the city of Zlatoust, craftsmen released a limited series of silver and gold commemorative coins, engraved with "In Trump We Trust."

CAMPAIGN SPEECHES

Trump's address revisited the themes of the campaign speeches that carried him to an improbable victory on November 8 over Democrat Hillary Clinton, who attended the ceremony with her husband, former President Bill Clinton.

Trump signalled the possibility of a more aggressive approach to Islamic State militants.

"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 said.

After repeating the 35-word oath of office, Trump stretched his arms wide and hugged his wife, Melania, and other members of his family. Ceremonial cannon blasts fired.

The transition from a Democratic president to a Republican took place before a crowd of former presidents and dignitaries.

Obama headed to a vacation in Palm Springs, California, after the ceremony. Before sitting down to lunch in the Capitol's Statuary Hall, Trump shook hands with both Clintons.

Trump takes office with work to do to bolster his image.

An ABC News/Washington Post poll this week found only 40 per cent of Americans viewed him favourably, the lowest rating for an incoming president since Democrat Carter in 1977, and the same percentage approved of how he has handled the transition.

Trump's ascension to the White House, while welcomed by Republicans tired of Obama's eight years in office, raises a host of questions for the United States.

Trump campaigned on a pledge to take the country on a more isolationist, protectionist path and has vowed to impose a 35 percent tariff on goods on imports from US companies that went abroad.

More than 60 Democratic lawmakers stayed away from the proceedings to protest Trump.

Many demonstrators are to participate in a "Women's March on Washington" on Saturday. Protests are also planned in other cities in the United States and abroad.

QUICK ACTION

Trump's to-do list has given Republicans hope that, since they also control the US Congress, they can quickly repeal and replace Obama's signature health care law, approve sweeping tax reform and roll back many federal regulations they say are stifling the US economy.

 

"He's going to inject a shock to the system here almost immediately," Trump senior adviser Kellyanne Conway told Fox News.

Democrats, in search of firm political footing after the unexpected defeat of Clinton, are planning to fight him at every turn. They deeply oppose Trump's anti-immigrant rhetoric from the campaign trail.

Trump's critics have been emboldened to attack his legitimacy because his win came in the Electoral College, which gives smaller states more clout in the outcome. He lost the popular vote to Clinton by about 2.9 million.

Trump's critics also point to the conclusion of US intelligence agencies that Russia used hacking and other methods during the campaign to try to tilt the election in the Republican's favour. Trump has acknowledged the finding - denied by Moscow - that Russia was behind the hacking but said it did not affect the outcome of the election.