(Adds Trump tweet)
By Jeff Mason and Makini Brice
Dec 5 (Reuters) - U.S. President Donald Trump headed to Georgia on Saturday for a rally aimed at boosting two Republican senators facing January runoffs, but some in his party worried he could end up hurting them by focusing on efforts to overturn his own loss on Nov. 3.
The Republican Trump has not conceded his defeat to Joe Biden, instead repeatedly and without evidence asserting widespread fraud. His claims have been rejected by state and federal officials across the country, and his campaign's numerous legal challenges have almost all failed.
Trump has also attacked Republicans who have refused to back him, including Georgia's governor, Brian Kemp, and its secretary of state, Brad Raffensperger.
Biden was the first Democratic presidential candidate to win in the southern state since 1992. Statewide recounts, including a painstaking review by hand of some 5 million ballots, turned up no significant irregularities.
On Saturday, Trump phoned Kemp and pressured him on Twitter to take further steps to benefit his candidacy.
"I will easily & quickly win Georgia if Governor @BrianKempGA or the Secretary of State permit a simple signature verification ... Why are these two 'Republicans' saying no?" Trump wrote on Twitter.
After Kemp responded on Twitter that he had "publicly called for a signature audit three times," Trump said that wasn't good enough, and added in a second tweet that the governor should immediately call a special session of the state legislature.
"Your people are refusing to do what you ask. What are they hiding?" Trump said.
In a move unprecedented in modern U.S. history, the Trump team has tried, without success, to get Republican-controlled legislatures in battleground states won by Biden to set aside the results and declare Trump the winner.
Biden won the election with 306 Electoral College votes - against the 270 required - to Trump's 232. The Electoral College will meet on Dec. 14 to formalize the outcome.
Trump's penchant for making his political rallies all about him - and now, about his claims the U.S. electoral system is rigged - has raised concerns among some Republicans that his appearance in Georgia could end up turning voters away. It will be his first post-election rally.
Matt Towery, a former Georgia Republican legislator who is now a political analyst and pollster, said Trump could help Republicans if he talks about the candidates, but warned:
"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."
Kemp will not attend Trump's rally scheduled for 7 p.m. EST in Valdosta, in rural southern Georgia, according to the Atlanta Journal-Constitution, one day after the death in a car crash of Harrison Deal, a close family friend of the governor and staffer for Georgia Senator Kelly Loeffler.
The Jan. 5 runoffs pit two Republican senators, David Perdue and Loeffler, against well-funded Democratic challengers Jon Ossoff and Raphael Warnock seeking to capture a state that has not elected a Democratic senator in 20 years.
The races will determine which party controls the U.S. Senate. Democrats need to gain both seats to seize a majority. If Republicans win one seat, they will retain control and be able to block much of Biden's legislative agenda.
Two pro-Trump lawyers, L. Lin Wood and Sidney Powell, have argued that Georgians should not vote in the runoff until issues from the 2020 election are resolved in the state, even after lawsuits they have filed to overturn the results have failed.
Trump's refusal to concede has forced Loeffler and Perdue to walk a fine line. Even as they warn voters of the dangers of a Democratic Senate majority, they will not say Biden won the White House.
They are not alone in their reticence. After contacting all 249 Republicans in the U.S. House and the Senate, The Washington Post said 220 of them would not say who won the election. Two said they considered Trump the winner.
Trump said on Twitter he wants the names of those who conceded to the newspaper that Biden was president-elect. (Reporting by Joseph Ax in Princeton, New Jersey and Makini Brice and Steve Holland in Washington; Writing by Sonya Hepinstall; Editing by Mary Milliken, Chizu Nomiyama and Daniel Wallis)