PHOENIX — President Trump on Thursday endorsed investor Blake Masters in the crowded Republican Senate primary in Arizona, siding with another acolyte of tech investor Peter Thiel after the former president’s support helped “Hillbilly Elegy” author James David Vance secure the GOP nomination in Ohio last month.

Mr. Trump, in a statement announcing his decision, called Mr. Masters a “great modern-day thinker” and slammed Mr. Masters’s chief rival Mark Brnovich. Mr. Trump criticized Mr. Brnovich, who is currently Arizona’s attorney general, for doing too little to promote Mr. Trump’s claims about the 2020 White House election he lost.

Republicans hope the winner of the August 2 primary can unseat Senator Kelley, who faces no major opposition for the Democratic nomination, and flip control of the Senate back to the GOP in one of the most closely contested general election races in November.

Mr. Trump’s endorsement could shake up a primary campaign that is without a clear front-runner and is largely defined by jockeying for Mr. Trump’s backing. Despite his re-election loss to President Biden, Mr. Trump remains popular with his party’s core supporters.

Mr. Masters, 35, has been a fierce critic of the technology industry where he built his career and has given voice to the cultural grievances that animate GOP base voters. He has called for reducing legal immigration and has claimed that Democrats are trying to ”replace Americans who were born here.”

Mr. Masters, who grew up in Tucson and moved back to southern Arizona in 2018, was until recently a senior executive for Mr. Thiel’s investment firm and foundation. Mr. Masters is making his first run for political office.

He gained notoriety in some circles for his detailed notes on a class Mr. Thiel taught at Stanford University. The two collaborated on the 2014 book, “Zero to One: Notes on Startups, or How to Build the Future,” and Mr. Masters went to work for Mr. Thiel. He rose to chief operating officer of Thiel Capital and president of the Thiel Foundation.

Mr. Trump, who has long hyped the power of his endorsements and held up his record as a measure of his ongoing hold on the Republican Party, has been bruised by a series of losses in early primary races in recent weeks.

Last month, Georgia voters rejected Mr. Trump’s efforts to punish the Republican governor and secretary of state, both of whom rebuffed Mr. Trump’s extraordinary efforts to overturn the results of the 2020 presidential election. Mr. Trump’s chosen candidates lost in Nebraska, Idaho, and North Carolina.

In Pennsylvania, the Senate primary that pitted Trump-endorsed celebrity heart surgeon Mehmet Oz against a former hedge fund CEO, David McCormick, is in the midst of a recount.

The former president does, however, have some major wins, particularly in Ohio last month, where Mr. Vance spiked in the polls after Mr. Trump’s endorsement in the Senate race.

Mr. Trump is counting on the next round of major primaries to counter perceptions that his influence over the Republican Party is waning as he lays the groundwork for a 2024 presidential run.

In addition to the Arizona Senate race, Mr. Trump is targeting Representative Cheney of Wyoming, a chief Trump critic who voted for his impeachment and is the top Republican on the House committee investigating the attack on the Capitol on January 6, 2021. Mr. Trump held a rally last weekend in the state to boost Ms. Cheney’s primary challenger, Harriet Hageman, who is currently far ahead in the polls.

Mr. Trump had long been expected to endorse Mr. Masters. Like Mr. Vance, Mr. Masters is a Thiel protégé whose campaign has received millions in support from the tech billionaire, who co-founded PayPal and was an early investor in Facebook. Many had expected Mr. Trump to make his support official after Mr. Vance’s win.

“Despite having such an amazing business career and wonderful family, Blake has decided that he wants to make a difference for the people of our Country,” Mr. Trump said in a statement endorsing Mr. Masters.

He said Mr. Masters would be strong on border security and gun rights, would cut taxes and regulations, and would support the military.

Mr. Masters, in response, said in a statement, “I wish everyone could know how this feels.” He said that “soon we will have a young, fearless, dynamic America First coalition in the U.S. Senate.”

As in most contested Republican primaries, Mr. Trump’s Arizona endorsement is a prize that was the subject of intense positioning by most of the candidates. Several, including Mr. Masters, made multiple trips to Mr. Trump’s Mar-a-Lago home in Florida and sought favor with the former president’s advisers. Last summer, businessman Jim Lamon, in a bid to draw Mr. Trump’s attention, aired an ad on Fox News in the New York-New Jersey market while Mr. Trump was staying at his golf course in Bedminster, New Jersey.

Mr. Trump in April ruled out backing Mr. Brnovich, who has opened a criminal investigation into the 2020 election in Arizona’s largest county after claims of fraud by Mr. Trump and his allies based on conspiracy theories and misleading data. Mr. Brnovich has trumpeted some of the allegations, claiming they raise questions about that election, but he did not deliver what Mr. Trump wanted most: indictments of election workers.

Mr. Trump again attacked Mr. Brnovich in his statement endorsing Mr. Masters, repeating the falsehood that the election in Arizona was “rigged and stolen.”

Mr. Trump has made a habit of announcing his endorsements just days or weeks before major races. That can add to the drama, but it also gives the campaigns he supports little time to publicize his endorsement. Mr. Trump has noted in the days after the Pennsylvania primary that his endorsement of Dr. Oz came “very late, many days AFTER Early Voting began,” suggesting he may have come to recognize that impact of his timing.

A former Arizona National Guard adjutant general, Michael McGuire, and a state utility regulator, Justin Olson, also are running for the Senate nomination.

The incumbent Mr. Kelly is a retired astronaut who became well-known in the state when his wife, Representative Giffords, was shot and critically wounded at a constituent event in Tucson in 2011. Mr. Kelly was elected last year to finish the last two years of the late John McCain’s term and is now seeking a full six-year term.

Once a GOP stronghold, Arizona has become a battleground thanks to a growing Latino population, an influx of more moderate newcomers and Republicans’ struggles with suburban women during the Trump presidency.

The race will serve as a test of how enduring those Democratic gains will be. Polls show Mr. Biden’s approval rating floundering and voters frustrated with steep inflation and rising gas prices.

A powerful spending group that has clashed with Mr. Trump in recent weeks, The Club for Growth, spending millions backing rivals of several of his chosen candidates, praised Mr. Trump’s decision in Arizona.

The organization’s president, David McIntosh, said that when the group and Trump work together, “real conservatives win, and that’s exactly what will happen in Arizona.”