"There has been no specific requests, but we are prepared to shoulder such costs after consultations", he said, adding the products with tampered documentation account for about four per cent of the sales in the affected businesses.
On Thursday, Kawasaki acknowledged that trust in his firm has "fallen to zero".
He said the company was focusing on pinpointing the cause of the problem, how to fix it and on confirming the safety of the products affected.
"Combined with previously announced clients, it will total about 500 firms", Yoshihiko Katsukawa, a senior Kobe Steel executive, told a press conference.
Crisis-hit Kobe Steel Ltd said on Friday its steel division has also falsely labelled products, the latest in a string of revelations confirming widespread cheating at the firm that has engulfed its global customers.
The new estimate comes as Kobe Steel's battered stock fell nearly nine per cent to finish at ¥805 (US$7.20), down more than 40 per cent since the start of the week after it admitted falsifying strength and quality data for a string of products - a practice it said may have started a decade ago.
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Boeing Co, has some of the falsely certified products, a source with knowledge of the matter told Reuters, but stressed that the world's biggest maker of passenger jets does not as yet consider the issue a safety problem.
More than thirty non-Japanese clients, including Daimler and Airbus to name a few, had been affected by the company's data fabrication.
Faulty parts have also been found in Japan's famous bullet trains that run at speeds as high as around 300km (180 miles) per hour and a space rocket that was launched in Japan earlier this week.
"There's a possibility that there will be new cases of wrongdoing", Kawasaki said.
In the United States, General Motors said that it did use aluminum from Kobe Steel "in certain models and we are working with Kobe to understand the potential impact".
The head of Japan's Kobe Steel (Other OTC: KBSTF - news) warned Thursday that a quality control scandal engulfing his firm was likely to widen at home and overseas, as he acknowledged that trust in the steelmaker has "fallen to zero".