The stock dived 22% on Tuesday to finish at 1,068 yen ($9.50), its maximum daily loss limit-wiping nearly a billion dollars off the firm's market value.
One customer, Central Japan Railway 9022.T , said some parts it received from Kobe Steel for its bullet trains did not meet Japanese Industrial Standards, but there were no safety issues.
General Motors, Boeing and Toyota are among the firms checking their models.
The country's trade ministry also wants Kobe Steel to provide reasons for the data fabrication and prevention measures within a month, Mr Kawasaki told reporters after meeting with the ministry.
"It seems in some cases quality control was undertaken by veteran employees who had lots of experience, highly trusted within the organisation, and somehow these discrepancies slipped by them", company spokesperson Gary Tsuchida said. Faced with the latest in a series of missteps that have undermined Japan's reputation for high-quality production, the industry ministry instructed Kobe Steel to assess the safety impact from the scandal.
Shares in Kobe Steel fell by almost 40% in two days, wiping more than $1.5bn (£1.1bn) off its market value after the firm admitted fabricating data about the strength and durability of products it delivered to more than 200 companies.
They include cases of falsified data at Nissan Motor and Mitsubishi Motors, while air bag maker Takata filed for bankruptcy in June over faulty airbags which were blamed for several deaths and many injuries.
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Kobe Steel faces potential costs from any product recalls, replacements and possible litigation, including class-action suits in the United States, Yuji Matsumoto, an analyst at Nomura Securities, said in a report. Conglomerate Toshiba Corp 6502.T is still battling the fallout of a scandal over reporting inflated profits.
Investors have also rushed to unload Kobe Steel's bonds, causing the extra yield demanded to hold the securities over Japanese government notes to jump.
Auto giant Toyota has already said Kobe Steel supplied materials to one of its Japanese factories, which used them in hoods, rear doors and surrounding areas of certain vehicles.
It's not the first time Kobe Steel has been caught up in falsifying data. Kobe Steel said it had failed to carry out tests it had agreed to conduct, and improperly "rewrote" inspection data. And in 2006, Kobe Steel said its Kakogawa steelworks in western Japan falsified soot emissions data over five years.
Iron ore powder is mainly used in making automobile components, according to Kobe Steel.
The steelmaker reported losses in the last two financial years, but has said it expects to return to profit this year. Kobe's steel business would fetch roughly 200 billion yen (US$1.78 billion), he said.