Boeing’s largest union rejected a tentative labor contract on Wednesday, a blow to the aerospace manufacturer and the Biden administration, which had intervened in the hopes of ending an economically damaging strike that began more than five weeks ago.

The contract, the second that workers have voted down, was defeated by a wide margin, with 64 percent of those voting opposing the deal, according to the union, the International Association of Machinists and Aerospace Workers. The union represents about 33,000 workers, but it did not disclose how many voted on Wednesday.

“This wasn’t enough for our members,” said Jon Holden, president of District 751 of the union, which represents the vast majority of the workers. “They’ve spoken loudly and we’re going to go back to the table.”

The vote is a setback for Boeing’s new chief executive, Kelly Ortberg, who is trying to restore Boeing’s reputation and business, which he described in detail earlier on Wednesday. In remarks to workers and investors, Mr. Ortberg said Boeing needed to undergo “fundamental culture change” to stabilize the business and to improve execution.

“Our leaders, from me on down, need to be closely integrated with our business and the people who are doing the design and production of our products,” he said. “We need to be on the factory floors, in the back shops and in our engineering labs. We need to know what’s going on, not only with our products, but with our people.”

Mr. Ortberg delivered that message alongside the company’s quarterly financial results, which included a loss of more than $6.1 billion. This month, Boeing also announced plans to cut its work force by about 10 percent, which amounts to 17,000 jobs. Boeing also recently disclosed plans to raise as much as $25 billion by selling debt or stock over the next three years as it tries to avoid a damaging downgrade to its credit rating.