Donald Trump drives by supporters at Million Maga March in Washington

US President has yet to present evidence that fraud allowed Joe Biden to win the November 3 election

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President Donald Trump gave supporters a drive-by wave on Saturday as hundreds gathered in Washington to push the discredited theory that fraud denied him rightful victory in the election.

Mr Trump expressed his thanks and suggested he might "stop by and say hello" ahead of the rallies held under the banners of "Stop The Steal", "Million Maga March" and "Women for America First".

Videos shared on social media showed the president's motorcade pull through the demonstration as a smiling Mr Trump waved at ecstatic crowds of supporters.

"I just want to keep up his spirits and let him know we support him," one loyalist, Anthony Whittaker of Winchester, Virginia, said outside the Supreme Court.

Marchers included members of the right-wing Proud Boys militia, prompting a large security presence to prevent clashes with separate anti-Trump events that were scheduled outside the Supreme Court.

The march was largely peaceful during the day before turning tense at night, with some confrontations along the margins as rival protests heckled Trump supporters with chants of “You lost!”

And several police lines blocked Trump supporters from entering the Black Lives Matter Plaza area as night fell.

Earlier, rump supporters chanted “USA, USA” and “four more years” and many carried American flags and signs to show their displeasure with the vote tally.

"The whole system's rigged ... in the way that the information is getting to the people, it's filtered through these channels that makes it so that the truth never actually gets out," said marcher Darion Schaublin, 26, who drove to Washington from Columbus, Ohio.

"There is a good chance ... he is not going to have a second term – and I'm not sure of the legitimacy of that."

The final two undeclared states were called on Friday by US television networks – with Democrat challenger Joe Biden winning the former Republican stronghold of Georgia in an extremely close race, and Mr Trump getting North Carolina.

The latest tallies give Mr Biden a solid overall final win in the state-by-state Electoral College that decides the presidency, with 306 votes against Trump's 232. In total, 270 votes are required for election.

President Trump continues to impede Mr Biden's ability to prepare for his transition before inauguration on January 20 and has filed numerous lawsuits – so far unsuccessfully – to challenge vote counts across the country.

On Friday, a judge in Michigan issued another rejection of Republican claims of fraud.

Mr Trump said on Friday that "time will tell" if he remains president, in a momentary slip of his unprecedented refusal to concede his election defeat and help Mr Biden prepare to take power.

The president broke his silence after a week with no on-camera comments, speaking at a Rose Garden event to herald the imminent authorisation of a coronavirus vaccine.

During a short speech about the vaccine work, Mr Trump insisted that he would never again call for a lockdown to curb the virus's spread.

Then he said: "Whatever happens in the future, who knows which administration it will be, I guess time will tell."

The hint of doubt came despite him continuing to claim that mass fraud – for which no evidence has been produced – robbed him of victory in the November 3 election.

Despite his own intelligence officials' declaration on Thursday that the election was "the most secure in American history", Mr Trump and his right-wing media allies show no sign of giving up their quest to get the results overturned.

"President Trump believes he will be President Trump, have a second term," spokeswoman Kayleigh McEnany said on Fox News.

Mr Biden is steadily preparing for power, with many world leaders congratulating him on his victory.

China was the latest nation on board, with a foreign ministry spokesman saying "we express our congratulations".