Senator Bill Cassidy, the Louisiana Republican whose 2021 vote to remove President Trump from office put a political target on his back, fought to hang on Saturday to a chance to defend his seat from a primary challenger backed by Mr. Trump.

In a perilous sign for Mr. Cassidy, his Trump-endorsed challenger, Representative Julia Letlow, had a sufficient lead to advance to a runoff election, according to The Associated Press.

Mr. Cassidy was trailing John Fleming, the state treasurer and a former Trump administration official, and as of late Saturday it was not yet clear who would secure the second-place finish and join Ms. Letlow in the runoff on June 27.

The result extended a bitter intraparty contest between Mr. Cassidy, who is seeking a third term and his challengers.

A runoff had been widely expected, but Mr. Cassidy’s chances of earning enough support to compete in it had been far from assured given Mr. Trump’s aggressive efforts to defeat him. Though polls were inconsistent, they had generally suggested a tight three-way race among Mr. Cassidy, Ms. Letlow and Mr. Fleming, with the senator appearing to trail the pack.

For Mr. Cassidy, who voted to convict Mr. Trump at his 2021 impeachment trial for inciting insurrection and has clashed with the Make America Healthy Again movement over vaccines, advancing to the runoff would be the first step in an uphill climb to keep his political career alive.

Mr. Cassidy, an incumbent with a powerful committee chairmanship and millions of dollars in his campaign war chest, has struggled to overcome what many in his party viewed as his disloyalty to Mr. Trump over his impeachment vote.

That opened what turned out to be an irreparable rupture between the president and Mr. Cassidy, which extended to many of his constituents back home. As voters headed to the polls Saturday morning, Mr. Trump attacked Mr. Cassidy in a social media post as a “disloyal disaster” and a “sleazebag.”

Mr. Cassidy had taken steps to try and repair his relationship with the president, and his voting record during Mr. Trump’s second term has hewed largely to Mr. Trump’s priorities. He has insisted the race is about “the present and the future,” even as Mr. Trump has been fixated on the past.

In a notable attempt at rapprochement, Mr. Cassidy, a gastroenterologist and strong proponent of vaccines who leads the Senate health committee, reluctantly backed Mr. Trump’s choice for health secretary, the vaccine skeptic Robert F. Kennedy Jr.

But the move failed to quell Mr. Trump’s anger, and the uneasy embrace did not create a lasting alliance between Mr. Cassidy and Mr. Kennedy, who enjoys backing from a powerful movement that has become a potent piece of Mr. Trump’s coalition and invested heavily in beating Mr. Cassidy.

Mr. Trump’s and Mr. Kennedy’s supporters are expected to coalesce behind Ms. Letlow, who also has the backing of the state’s governor, Jeff Landry.

Ms. Letlow, who has a relatively low profile statewide, spent the final weeks of the race focused on attacking Mr. Fleming, who polls had shown would be a tougher opponent in a runoff. Mr. Cassidy may have benefited from a split among the state’s most conservative voters between his two main opponents.

As he sought to keep his political career alive, Mr. Cassidy’s campaign and groups supporting him spent more than $21 million on ads, many of them attacking Ms. Letlow as overly liberal. In recent weeks, he highlighted a video in which she voiced support for diversity, equity and inclusion initiatives as she was interviewing for a job as a university president.

Mr. Fleming, who spent eight years in Congress and is a former Trump administration official, seized on those statements as he tried to cut into Ms. Letlow’s support with voters loyal to the president.