Russian President Vladimir Putin has congratulated Joe Biden on his victory in the US presidential election after Biden won the state-by-state electoral college vote that officially determines the US presidency.

The Kremlin had said it would wait for the official results of the election before commenting on its outcome, even as other nations congratulated Biden on the win in the days after the November 3 vote.

“For my part, I am ready for interaction and contact with you,” the Kremlin cited Putin as saying in a statement on Tuesday.

“Putin wished the president-elect every success and expressed confidence that Russia and the United States, which have a special responsibility for global security and stability, could, despite their differences, really help to solve the many problems and challenges facing the world,” the Kremlin said.

Mr Biden came out swinging in a national address just hours after the vote, Mr Biden urged Americans to “turn the page” on the Trump era.

“The flame of democracy was lit in this nation a long time ago,” he said in a nationally televised speech late on Monday (US time).

“We now know that nothing – not even a pandemic or an abuse of power – can extinguish that flame.

“In this battle for the soul of America, democracy prevailed.”

The Electoral College vote, typically a formality in US elections, assumed outsized significance because of President Donald Trump’s extraordinary effort to subvert the process due to what he has falsely alleged was widespread voter fraud.

Some Trump supporters had called for protests on social media and election officials had expressed concern about the potential for violence amid the President’s heated rhetoric.

But Monday’s vote proceeded smoothly, with no major disruptions.

California, the most-populous US state, put Mr Biden over the 270 votes needed to win the Electoral College when its 55 electors unanimously cast ballots for him and running mate Kamala Harris.

Tweet from @KamalaHarris

Mr Biden and Ms Harris – the first woman, first black person and first Asian American to become vice president-elect – will be sworn in on January 20.

Mr Biden earned 306 electoral votes in November compared with 232 for Mr Trump.

In 2016, when Mr Trump beat Hillary Clinton to be president, he also won 306 electoral votes.

“At the time, President Trump called the Electoral College tally a landslide,” Mr Biden said.

“By his own standards, these numbers represented a clear victory event and I respectfully suggest they do so now.”

Tweet from @JoeBiden

In 2016, Mr Trump lost the national popular vote by nearly 3 million ballots. Mr Biden won the popular vote in November by more than 7 million votes.

With Mr Trump’s legal challenges floundering, his dim hopes of clinging to power rest in persuading Congress not to certify the Electoral College vote in a January 6 session – an effort almost certain to fail.

Mr Biden urged the outgoing President to accept the election result.

“Every single avenue was made available for President Trump to contest the results. He took advantage of each of them. President Trump was denied no course of action he wanted to take,” he said.

“Respecting the will of the people is at the heart of our democracy. Even when we find those results hard to accept.”

Mr Trump – who is yet to respond publicly to the Electoral College vote – had also pressured Republicans in battleground states that Mr Biden won, such as Pennsylvania and Michigan, to set aside the vote totals and appoint their own competing slates of electors.

However they largely dismissed the notion.

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“I fought hard for President Trump. Nobody wanted him to win more than me,” Lee Chatfield, Republican speaker of the Michigan House of Representatives, said in a statement.

“But I love our republic, too. I can’t fathom risking our norms, traditions and institutions to pass a resolution retroactively changing the electors for Trump.”

In Arizona, at the beginning of the electors’ meeting there, the state’s Democratic secretary of state, Katie Hobbs, said Mr Trump’s claims of fraud had “led to threats of violence against me, my office and those in this room today”, echoing similar reports of threats and intimidation in other states.

That echoed comments in early December from a senior Republican official in Georgia. In an impassioned plea, Gabriel Sterling warned Mr Trump “it’s all gone too far”, while revealing his fear that “someone is going to get hurt”.

-with AAP