Many expressed hope that Biden would right the world's largest democracy after they watched rioters storm the US Capitol, shaking the faith of those fighting for democracy in their own countries.

German Chancellor Angela Merkel praised the swearing-in ceremony as "a true celebration of American democracy".

"I look forward to a new chapter of German-American friendship and co-operation," tweeted her spokesman Steffen Seibert, who quoted the chancellor on Twitter.

Canadian Prime Minister Justin Trudeau, who butted heads with Trump over trade, said that "Canada and the United States enjoy one of the most unique relationships in the world".

He said he looked forward to working with the new administration to promote climate action, clean economic growth, inclusion and diversity.

French President Emmanuel Macron noted the urgency of addressing climate change after Trump withdrew the US from the Paris climate accord, a move Biden reversed in the first hours of his presidency.

"We will be stronger to face the challenges of our time. Stronger to build our future. Stronger to protect our planet," he wrote on Twitter.

"Welcome back to the Paris Agreement!"

NATO Secretary General Jens Stoltenberg called Wednesday "the start of a new chapter".

The 70-year-old Western military alliance was shaken by Trump's frequent criticism, who often cast it as a drain on US resources.

British Prime Minister Boris Johnson, who appeared to have a chummy relationship with Trump, congratulated Biden "on being sworn in as President of the United States" and Harris "on her historic inauguration" on Twitter.

In Brussels, top EU officials welcomed a new era of co-operation with Washington after four years of often being treated like a hostile ally.

"Like people of all nations, the American people deserve leaders who take their hopes and concerns to heart," EU Council President Charles Michel said, adding he trusted Biden and Harris to do "just that".

Italian Prime Minister Giuseppe Conte tweeted "this is a great day for democracy, reaching far beyond the American borders".

Brazilian President Jair Bolsonaro, an ally of Trump's, congratulated Biden and said he hoped the two countries could pursue a free-trade deal, in a letter posted on Twitter.

Prime Minister Jacinda Ardern said Biden was a good friend to New Zealand and highlighted in particular the words given in his inaugural address. "President Biden's message of unity as he takes office is one that resonates with New Zealanders," Ardern said.

South Korean President Moon Jae-in said: "America's new beginning will make democracy even greater."

Japanese Prime Minister Yoshihide Suga congratulated Biden and Harris and said he looked forward to "working with you and your team to strengthen our alliance and realise a free and open Indo-Pacific".

Israeli Prime Minister Benjamin Netanyahu, who enjoyed a warm relationship with Trump, also voiced optimism.

"I look forward to working with you to further strengthen the US-Israel alliance, to continue expanding peace between Israel and the Arab world and to confront common challenges, chief among them the threat posed by Iran," he said.

The Palestinians, meanwhile, hope Washington will dial down its pro-Israel stance.

Palestinian President Mahmoud Abbas expressed his readiness for "a comprehensive and just peace process that would achieve the wishes of the Palestinian people in freedom and independence."

Other nations also expressed cautious hope for a reset in relations before the inauguration.

China was hoping for "a collaboration beneficial to both sides", the foreign ministry in Beijing said, adding the country would maintain its own interests and would not be defamed by the US.

Meanwhile, arch-rival Iran said it was ready to clear its differences with the US. But the ball was in Washington's court, President Hassan Rouhani told state television on Wednesday.

Of the 2015 nuclear deal, Rouhani said if Biden was serious about fulfilling its international obligations towards Iran, Tehran would do likewise.

Pope Francis wished Biden - a devout Catholic - strength and wisdom.

"May Americans, under their leadership, continue to draw strength from the high political, ethical and religious values that have inspired the nation since its inception," he wrote in a message to the White House.

Australian Associated Press