Donald Trump puts his grievances at centre stage during Georgia campaign rally

US President Donald Trump pressed his own grievances over losing the presidential election at a rally in Georgia at the expense of the political battle for control of the Senate.

Thousands of largely maskless supporters gathered in Valdosta, shortly after Mr Trump was rebuffed by Georgia's Republican governor in his astounding call for a special legislative session to give him the state's electoral votes despite Joe Biden winning the majority of the vote.

The latest futile attempt to subvert the presidential election results continued his unprecedented campaign to undermine confidence in the democratic process, but overshadowed his stated purpose in boosting senators David Perdue and Kelly Loeffler.

Republicans need one victory to maintain their Senate majority, and Democrats need a Georgia sweep to force a 50-50 Senate and position Vice President-elect Kamala Harris as the tiebreaking majority vote.

Party officials had hoped the president would dedicate his energy to imploring their supporters to vote in the January 5 election, when Mr Perdue and Mr Loeffler try to hold off Democrats Jon Ossoff and Raphael Warnock respectively.

After Air Force One landed, it quickly became apparent Mr Trump's aim was to air his own complaints and stoke baseless doubts about the conduct of last month's vote, rather than boost his party.

"I want to stay on presidential," Mr Trump said minutes into his speech, "but I got to get to these two."

Mr Trump pulled out a piece of paper and read a list of his electoral achievements, including falsely asserting he won Georgia and the White House.

Mr Biden took the state by 12,670 votes and won a record 81 million votes nationally, but Mr Trump continued to reiterate his unsubstantiated claims of fraud, despite his own administration assessing the election to have been conducted without any major issues.

Hours before the event, Mr Trump asked Georgia Governor Brian Kemp in a phone call to order the legislative session, but the governor refused according to a senior government official in Georgia.

Mr Kemp, in a tweet, said Mr Trump also asked him to order an audit of signatures on absentee ballot envelopes in his state, a step he is not empowered to take because he has no authority to interfere in the electoral process on Mr Trump's behalf.

Mr Trump, though, vented his frustrations with Mr Kemp on Twitter and at the rally.

"Your people are refusing to do what you ask," he complained in a tweet, as if speaking with Kemp. "What are they hiding? At least immediately ask for a Special Session of the Legislature. That you can easily, and immediately, do."

At the rally, he took aim once again at Kemp, saying he could assure him victory "if he knew what the hell he was doing."