GREENVILLE, N.C. — As Republicans gathered Saturday in two battleground Southern states to chart a course forward after losing the White House and both chambers of Congress, former president Donald Trump was partially fixated on the past as he aired grievances, repeated falsehoods and promoted culture war issues that have captured his imagination.

Much of Trump’s focus at the state’s annual Republican convention here was on the 2020 election, his administration’s response to the coronavirus pandemic, his two impeachments and various investigations into him or his business as he sought to appeal to his most enthusiastic supporters, who showed up in force to see him speak.

“That election will go down as the crime of the century, and our country is being destroyed by people who perhaps have no right to destroy it,” he said, uttering a series of false statements about voter fraud in several states.

Trump’s appearance Saturday illustrates a continued conundrum for the Republican Party: While he remains overwhelmingly popular among the party’s faithful, he potentially poses a problem for the GOP as it looks to win over voters ahead of the 2022 midterms who are wary of his divisive style.

Some Republicans argue that the party needs to move past Trump to woo disaffected suburban voters and women with a return to a focus on policy. As evidence, they maintain that Trump contributed to Georgia Republicans losing both the state’s Senate seats in a January runoff because he would not budge from his false claims that the election was rigged rather than push the Republican candidates as a needed counter to President Biden’s agenda.

“There is no alternative to Trump right now because people are so afraid to challenge him in any way. There doesn’t seem to be a tremendous appetite for what Trump is selling outside of the MAGA faithful,” said Sarah Long­well, who leads Republican Voters Against Trump. “A lot of Republicans want to move on from Trump, but they need all the voters who have engaged on Trump’s behalf to stick with them.”

But the events this weekend showed that the concerns of some elected Republicans and party strategists aren’t shared by the party’s base of voters.

In Georgia, people attending the party’s state convention booed Republican Gov. Brian Kemp for not doing more to overturn the results of the 2020 election and formally censured Brad Raffensperger, the secretary of state who publicly bucked Trump and vouched for the veracity of Georgia’s election results.

In North Carolina, the crowd roared as Trump pushed false election fraud claims and even suggested that audits in states such as Pennsylvania, Georgia and Arizona could show that he won.

And while several Trump administration officials have said privately that his response to the coronavirus was the nadir of his presidency and probably cost him reelection, the crowd in North Carolina reveled in his insults of officials involved in the pandemic and his boasts that he did a great job.

“He’s not a great doctor, but a hell of a promoter. He likes television more than any politician in this room,” Trump said of frequent target Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, minutes after discussing what good ratings Trump himself receives.

There are few signs that Trump is losing his grip over the party’s base, and party leaders remain wary of crossing him or leveling even the slightest bit of criticism at the former president. One who did, Rep. Liz Cheney (R-Wyo.), was kicked out of her House leadership post last month. He is considered, at the moment, to be a lock for the party’s presidential nomination in 2024 if he runs again, which remains an uncertainty.

Saturday night’s speech was an entrance of sorts to what is expected to be a busy political summer for the former president. Trump is expected to speak to several more GOP state events and host rallies for candidates he supports — particularly those running against Republicans who voted to impeach him on charges that he incited the Jan. 6 attack on the Capitol. He recently held a fundraiser at his club in Bedminster, N.J., for his super PAC, which raised about $5 million, advisers said.

But there are signs Trump’s influence could erode.

None of the major cable stations carried his speech live.

Criminal investigations by the New York attorney general and Manhattan district attorney into his businesses are heating up — probes he preemptively decried as prosecutorial misconduct on Saturday night in a discursive rant against those who have investigated him.

Trump may decide he’s uninterested in another run for office or feels he’s better off focusing on his business, major aspects of which are struggling.

And Republican voters could make a slow turn to other candidates, as allies of Senate Minority Leader Mitch McConnell (R-Ky.) and many other potential 2024 presidential candidates hope will happen, if the repetitive nature of Trump’s attacks and rhetoric grow tiresome for some.

“It’s always packaged as Donald Trump delivering his greatest hits. It’s true in that room. When you get out of that room and you’re not part of the faithful you don’t like a lot of the songs,” said Doug Heye, a former Republican National Committee communications director and deputy chief of staff to former House Majority Leader Eric Cantor (R-Va.). “It’s those suburban areas seeing the population explode. How much longer can Republicans avoid dealing with that?”

Even some of Trump’s supporters said he needed to move on from the 2020 election.

“We just got to continue on because what’s [an election audit] going to change? We’re going to spend millions of dollars to change what?” said Aubrey Moreland, from Kingsland, Ga., a retired Navy veteran who attended the Georgia state convention.

When Trump made a surprise endorsement of Rep. Ted Budd (R-N.C.) in the Senate GOP primary in North Carolina, the candidate he opposed immediately came to the back of the room and said it would backfire.

“North Carolinians will make up their minds on their own,” said former North Carolina governor Pat McCrory, repeatedly arguing the room was “flat” when Trump announced the pick.

But in a nod to Trump’s continued sway over the party, McCrory immediately defended the former president — and blamed “Washington insiders who gave the president bad advice” for his surprise endorsement. “The president had a good message tonight,” he said.

South Dakota Gov. Kristi L. Noem, a potential Republican presidential candidate for 2024 who spoke in North Carolina before Trump, heaped praise on the former president. “I love that man,” she said.

Much of Trump’s speech seemed a fossilized version of the 2020 campaign trail. The rally playlist had all the mainstays — from Laura Branigan’s “Gloria” to Elton John’s “Tiny Dancer.” Many wore “Trump 2020” shirts. Trump showed up an hour late as an expectant crowd roared for him. He bashed Hunter Biden, President Biden’s son, for his business ties in Ukraine and went after Facebook and other big tech companies.

The former president’s advisers have repeatedly urged him to move his stump speeches from a focus on the 2020 election to the 2022 midterms and provide a fresh vision, according to people familiar with the discussions who spoke on the condition of anonymity to describe the private conversations.

On Saturday night, Trump attacked Biden for high gas prices, the surge of migrants at the border, rising crime and the economy as he read from the teleprompter.

Trump’s attempts at new attacks were met by a largely quiet room when he spent the first 45 minutes of his speech going after Biden without much excitement in his voice and the crowd barely clapped or rose to its feet.

But Trump’s two biggest applause lines of the night — saying China should be charged $10 trillion for the coronavirus originating in the country and that teaching critical race theory, an academic framework centered on the idea that racism is systemic, not just a collection of individual prejudices, should be banned — were not staples of his 2020 speeches.

He received potentially telling silence when repeatedly touting the coronavirus vaccine and telling the crowd it was his administration that was responsible for its quick development. Many Trump supporters, according to public polls, are skeptical of getting vaccinated.

But the former president seemed most animated when going after prosecutors investigating him in New York and vigorously contesting the election results, telling the crowd in detail how other states could still vindicate him.

“They’ll never stop until November 2024,” he said of prosecutors in New York, who are investigating his company for potential financial crimes.

He repeated a litany of falsehoods about the election, lashed into mail-in balloting and praised voting bills that have passed in Texas, Florida and other states — and criticized politicians in Georgia he despises for not going along with his requests to overturn the election result despite no evidence of widespread fraud.

In Georgia, as Kemp took the stage with his family, the jeers outnumbered the cheers as many attendees booed him and continued to make noise throughout his speech. Some held up signs for his opponent Vernon Jones, a former Democratic state representative who switched parties earlier this year.

“There could have been much more done and it should have been done in the beginning,” said Julie Scarborough, a first-time delegate from rural Cairo, Ga., explaining why she now opposes Kemp.

But the governor plowed through, focusing on the state’s response to covid, the economy and the heartbeat bill, one of the strictest abortion laws in the country when Kemp signed it in 2019 but that has since been ruled unconstitutional.

He didn’t mention the 2020 election.

Delegate Richard Finke from Gwinnett County, a suburban county of Atlanta, was attending his first convention. The retired U.S. Army and Life Flight helicopter pilot said he wanted to see an audit of the election in Georgia.

Although he still approves of 90 percent of what Kemp has done, Finke said, the governor isn’t currently his favored candidate for the next election.

Also firmly in Trump’s corner is Jones, whose fiery speech got a lot of applause and cheers from the audience, especially as he noted that, if elected, on day one he would replace the election machines and do a forensic audit.

At the end of his speech, Jones continued his attack on Washington. “We’re going to burn this house down,” he said.

Amy B Wang contributed to this report. Watson reported from Jekyll Island, Ga.