WASHINGTON - Democrat and Republican leaders campaigned in duelling rallies in Georgia on Monday (Jan 4) on the eve of the state's two run-off races which will determine control of the Senate, and with that, President-elect Joe Biden's ability to carry out his agenda.

But the election eve campaigning was at times overshadowed by outgoing President Donald Trump's ongoing attempt to overturn the result of November's presidential election, which he lost.

"That was a rigged election," Mr Trump said on Monday night at the start of his rally speech in Georgia, meant to drum up support for Republican incumbents David Perdue and Kelly Loeffler, who are facing off against their Democrat challengers Jon Ossoff and Raphael Warnock.

"If the liberal Democrats take the Senate and the White House - they're not going to take this White House, I'm going to fight like hell," said Mr Trump, who spent the rally raising conspiracy theories, repeating disproven claims of electoral fraud, and lamenting the refusal of some Republican allies to object to the election results.

The Democratic Party must win both of Tuesday's races to gain control of the Senate. But also looming is Wednesday's formal certification of states' electoral votes in Congress to confirm Mr Biden's victory.

Mr Biden travelled to Georgia on Monday afternoon to rally in support of Mr Warnock and Mr Ossoff, arguing that their election would break the gridlock in Washington and enable the Democrats to make progress on jobs, healthcare, justice and the environment.

Most immediately, having Mr Warnock and Mr Ossoff's votes in the Senate could enable Democrats to roll out the US$2,000 (S$2,640) Covid-19 stimulus cheques, Mr Biden said. Republicans oppose the cheques, although Mr Trump does not.

Mr Biden also criticised Mr Perdue and Ms Loeffler for attempting to subvert the Constitution and America's democracy in backing Mr Trump's attempts to reverse his loss.

"You have two senators who think they've sworn an oath of office to Donald Trump, not the United States Constitution," said Mr Biden.

"Politicians cannot assert, take, or seize power. Power has to be given, granted - by the American people," he added.

Mr Trump is treating Wednesday's session of Congress as his final option to overturn the election and demanding that Republican allies aid in the effort. A group of Republicans, including Senators Ted Cruz and Josh Hawley, have said they will contest the certification, but they do not have the numbers to succeed.

Other Republicans including Senate majority leader Mitch McConnell have objected, largely on the grounds that for Congress to overturn electoral votes certified by the states would be undemocratic and unconstitutional.

At Monday's rally, Mr Trump expressed his displeasure with Republicans - whom he has called the "Surrender Caucus" on Twitter - who were not on board with him.

"I'll be back here in a year and a half campaigning against your governor... and your crazy secretary of state," he said of Georgia governor Brian Kemp and secretary of state Brad Raffensperger.

Both are lifelong Republicans once championed by Mr Trump, but who have refuted his claims of voter fraud and his pressures to deny the election result, most recently Mr Raffensperger, who did so in a phone call with Mr Trump last Saturday that was leaked.

Mr Trump also lamented that Supreme Court Justices whom he appointed were "not stepping up to the plate" in not accepting his legal challenges. He also said he wanted Vice-President Mike Pence, who will preside over Wednesday's Congress session, to help in overturning the results of the election.

"I hope Mike Pence comes through for us," said Mr Trump at the Georgia rally. "If he doesn't come through, I won't like him quite as much."

Republicans, however, have expressed fears that Mr Trump's mixed messaging and insistence of rampant fraud might discourage Republican voters from turning out to vote on Tuesday.

"This is all easily, provably false, yet the President persists, and by doing so undermines Georgians' faith in the election system," said Georgia elections official Gabriel Sterling on Monday, in a press conference where he systematically debunked Mr Trump's claims of fraud.

"Given the nature of the President's statements... we are specifically asking and telling you to turn out and vote tomorrow," said Mr Sterling, a lifelong Republican. "Do not self-suppress your own vote."

The political turmoil has America on edge. In a letter released on Monday, more than 170 leaders from prominent businesses including Pfizer and Microsoft, urged Congress to accept the electoral college results.

Pro-Trump supporters are gathering in Washington, DC, ahead of Wednesday's Congress session, with the capital city's mayor urging residents to stay home and activating the National Guard over fears of protests turning violent.

Leader of the Proud Boys far-right group Enrique Tarrio was arrested on Monday shortly after he arrived in DC, over charges of property destruction from a protest the month before.