Donald Trump returned to the campaign trail on Saturday – not, notionally at least, in his quixotic and doomed attempt to deny defeat by Joe Biden, but in support of two Republicans who face January run-offs which will decide control of the US Senate. The president and first lady Melania Trump appeared at a regional airport in Valdosta, in Lowndes county in southern Georgia, a staunchly Republican region. Trump reminded the chanting crowd that he came to southern Georgia on behalf of the two senators facing runoffs. But he quickly turned to his repeated claims, made without evidence, of widespread fraud in the presidential election. “They cheated and rigged our presidential election but we’ll still win it. And they are going to try to rig this election too,” Trump told the crowd, who chanted “We love you!” and “Four More Years!” Trump’s claims have been rejected by state and federal officials across the country, and his campaign’s numerous legal challenges have almost all failed. Republican governor Brian Kemp was strongly backed by Trump in his run for office in 2018 but he was not expected to attend on Saturday. The governor has drawn Trump’s ire after certifying a state contest Biden won by more than 10,000 votes. It was reported on Saturday that Trump had called Kemp from the White House, to ask him to overturn the Georgia result. Kemp reportedly declined. Trump persisted, tweeting that Kemp should “immediately ask for a special session of the legislature”. As the crowd at the rally chanted “stop the steal”, Trump said: “Your governor could stop it very easily if he knew what the hell he was doing.” According to a tweet from Kemp, Trump also asked him to order an audit of signatures on absentee ballot envelopes in his state, a step Kemp is not empowered to take because he has no authority to interfere in the electoral process on Trump’s behalf. Trump has repeatedly tied the Georgia runoffs to his baseless accusations of electoral fraud in key states, claims he insisted on Friday would inspire Republicans in Georgia ahead of the Senate run-offs. “Spirits will soar and everyone will rush out and VOTE!” he wrote. To the contrary, many observers postulate that Trump’s baseless claims that the election was rigged could depress Republican turnout, handing a vital advantage to Jon Ossoff and Raphael Warnock, the Democratic challengers to senators Kelly Loeffler and David Perdue. If Ossoff and Warnock win, the Senate will be split 50-50, Kamala Harris’s vote as vice-president giving Democrats control. Polling in both races is tight. Trump’s recalcitrance is being encouraged by congressional Republicans. On Saturday the Washington Post reported that only 26 of 249 GOP representatives and senators had acknowledged Biden’s victory. Biden won the electoral college by 306-232, the result Trump said was a landslide when it favoured him over Hillary Clinton. Biden is more than 7m ballots ahead in the popular vote, supported by more than 81 million Americans, the most of any candidate for president. But Democrats performed less well in Senate, House and state elections, making the Georgia runoffs vital to the balance of power as leaders look to agree stimulus and public health measures to tackle the Covid-19 pandemic and its attendant economic downturn. Earlier this week, two lawyers who have been involved in legal challenges to Biden’s victory and have trafficked in outlandish conspiracy theories, Lin Wood and Sidney Powell, told Trump supporters not to vote in Georgia unless Republican leaders act more aggressively to overturn the presidential result. “We’re not gonna go vote 5 January on another machine made by China,” Wood said on Wednesday. “You’re not gonna fool Georgians again. If Kelly Loeffler wants your vote, if David Perdue wants your vote, they’ve got to earn it. They’ve got to demand publicly, repeatedly, consistently, ‘Brian Kemp: call a special session of the Georgia legislature’. “And if they do not do it … they have not earned your vote. Don’t you give it to them. Why would you go back and vote in another rigged election?” After a rush of defeats on Friday, Trump has won one election lawsuit and lost 46. But he continues to attack, on Saturday slamming Kemp and secretary of state Brad Raffensperger for refusing to overturn a contest in which the state went Democratic for the first time since 1992. “Why are these two ‘Republicans’ saying no?” Trump asked. “If we win Georgia, everything else falls in place!” Matt Towery, a former Georgia Republican legislator now an analyst and pollster, told Reuters Trump could help in the state “if he spends most of his time talking about the two candidates, how wonderful they are, what they’ve achieved. If he talks about them for 10 minutes and spends the rest of the time telling everyone how terrible Brian Kemp is, then it will only exacerbate things.” Gabriel Sterling, the Republican manager of Georgia’s voting systems, this week blamed the president and his allies for threats of violence against election workers and officials. On Friday, he said: “I think the rhetoric they’re engaged in now is literally suppressing the vote.” At a rally in Savannah, the vice-president was greeted by chants of “stop the steal”. “I know we’ve all got our doubts about the last election,” Pence said, “and I actually hear some people saying, ’Just don’t vote.’ My fellow Americans, if you don’t vote, they win.” Kemp and Loeffler missed events on Friday after a young aide to the senator was killed in a car crash. Former president Barack Obama held a virtual event in support of Warnock and Ossoff. From Wilmington, Delaware, preparing to take power on 20 January, Biden said he would travel to Georgia at some point, to campaign with the Democratic candidates.