TOKYO—The reclusive chief executive of Takata Corp., the Japanese maker of air bags linked to at least eight deaths, made a long-awaited public appearance Thursday, saying the company was studying the possibility of a fund to compensate victims.

U.S. Sen. Richard Blumenthal (D., Conn.), during a congressional hearing this week, called on the company to establish such a fund, raising pressure on Takata as it confronts the biggest automotive recall in U.S. history, affecting 32 million vehicles. Kevin Kennedy, Takata's North American executive vice president, said at the hearing that he couldn't commit to establish such a fund. Sen. Blumenthal asked Mr. Kennedy to give the congressional panel an answer in two weeks on the matter.

At his first news conference ever, CEO Shigehisa Takada, 49 years old, apologized over the recalls, and for not speaking to the media until now. The recalls began in 2008, when he was president of the company, and escalated in mid-2014, after he became CEO and chairman.

"I felt that the priority of my job is to ensure our products are safe," he said. "I regret that I haven't offered enough explanations," he added, saying he wouldn't step down because he wants to resolve the problem.

Mr. Takada said a fund was only one option the company was considering for compensating victims, adding that he wouldn't promise any specific measure.

Mr. Takada has apologized earlier, at last year's shareholder meeting and in press statements.

Mr. Takada bowed deeply to open the news conference, which followed the company's annual shareholders' meeting in Tokyo. He spent much of the subsequent hour-and-a-half staring resolutely ahead as aides explained the details of the recall, which until recently has attracted far less attention in the company's domestic market than in the U.S., where government pressure has kept the company in the spotlight.

Mr. Takada and other executives offered little information to clear up the uncertainty over what, exactly, is causing Takata-made air bags to explode, or how high Takata's recall-related costs might climb.

Takata stuck with its ¥ 20 billion ($161.8 million) net profit outlook for this financial year, repeating it can't reasonably estimate how much it would end up paying. So far, the banks it deals with haven't expressed concerns about Takata's financial position, Mr. Takada said.

But recalls and associated costs to replace the inflaters—the components that contain an explosive chemical that deploys air bags in a crash—continue to expand.

In May, Takata agreed with the U.S. National Highway Traffic Safety Administration to nearly double recalls in the U.S.

On Thursday, three Japanese auto makers including Toyota Motor Corp. recalled around an additional 3 million vehicles world-wide, while in South Korea, Honda Motor Co. and three other auto makers and importers were ordered by the government to recall more than 24,000 vehicles.

"We will be discussing the costs with auto makers," said Chief Financial Officer Yoichiro Nomura.

The company also potentially faces class-action lawsuits in the U.S. and Canada.

Mr. Takada's absence from public view, until now, has prompted questions about whether he has been fully engaged with the air-bag problem. Mr. Takada, the grandson of the company's founder, took over as the head of Takata in 2011 after the death of his father, Juichiro, who developed Takata into one of the world's biggest automotive safety parts manufacturers.

Mr. Takada's mother Akiko, a former executive who is now an adviser, has been actively involved in some of Takata's key operations, two people knowledgeable about the matter said.

But Mr. Takada said Thursday that his mother wasn't making key decisions related to the recalls. That role, he said, was being filled by six top executives, including himself.

Mr. Takada and his mother are the biggest individual shareholders at Takata, controlling about 2.9% and 2.1% respectively, as of March. Also, 52.1% of Takata shares were held by TKJ Co., a Takada family investment vehicle.

Mr. Takada, addressing a concern raised repeatedly at the congressional hearing this week, said the company would continue to use ammonium nitrate as a main ingredient in the propellant of its air bag inflaters.

Takata is the only major maker of inflaters using ammonium nitrate, which is sensitive to temperature change and moisture. Rivals such as Autoliv, TRW and Daicel use a different chemical, guanidine nitrate, and, in addition to Takata, these companies are also producing replacement inflaters for vehicles that have been recalled over Takata air-bag problems.

Takata has produced roughly 200 million inflaters to date containing ammonium nitrate, said Hiroshi Shimizu, a senior executive in charge of quality. Takata believes the mix is safe, Mr. Takada said.

--In-Soo Nam in Seoul contributed to this article.

Write to Yoko Kubota at yoko.kubota@wsj.com and Eric Pfanner at eric.pfanner@wsj.com

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