Boeing’s largest union rejected a tentative labor contract on Wednesday by a wide margin, extending a damaging strike and adding to the mounting financial problems facing the company, which hours earlier had reported a $6.1 billion loss.

The contract, the second that workers have voted down, was opposed by 64 percent of those voting, 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.

“There’s much more work to do. We will push to get back to the table, we will push for the members’ demands as quickly as we can,” said Jon Holden, president of District 751 of the union, which represents the vast majority of the workers and has led in the talks. He delivered that message at the union’s Seattle headquarters to a room of members chanting, “Fight, fight.”

Boeing declined to comment on the vote, which was a setback for the company’s new chief executive, Kelly Ortberg, who is trying to restore its reputation and business with a strategy 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.”