He visited Akihiro Tada, director general of the ministry's Manufacturing Industries Bureau, and apologized for the data falsification having caused anxiety to many people.
The comments came as a growing list of customers, including major automakers Toyota, Nissan and Honda, scramble to assess the safety of vehicles containing products supplied by the company, which has admitted falsifying quality data for products sold to some 200 clients.
It was unclear what the impact would be on earnings, the company said in a statement.
"There are suspicious cases in Japan and overseas that could involve further wrongdoing, as the ongoing investigation has not been completed", Kawasaki told a press briefing on the matter, following a meeting with an official from the trade ministry.
Kobe Steel said late on Wednesday it found 70 cases of tampered data on materials used in optical disks and liquid crystal displays at its Kobelco Research Institute Inc, which makes and tests products for the company.
Shares in the company stabilised on Thursday after about $1.6bn was wiped off its market value in two days.
The chief executive of Kobe Steel Ltd. warned on Thursday that there may be further cases of falsified data than have been previously disclosed, in a widening scandal over its inspection data that has affected hundreds of companies.More news: Trump lashes out at Puerto Rico as House weighs aid package
Kobe Steel's admission this week sent shock waves through the global automotive and aerospace supply chains.
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.
Central Japan Railway said some Kobe Steel parts for its bullet trains did not meet Japanese industrial standards, but there were no safety issues.
The Japanese government wants the steelmaker to report on the result of its safety checks within two weeks.
West Japan Railway also found substandard Kobe aluminum parts in seven high speed trains made by Hitachi and Nippon Sharyo, according to West Japan Railway spokesman Shugo Nishimura. The company said about 4% of shipments between September 2016 and August 2017 were impacted, which was discovered by what it called an "emergency quality audit", but admitted the falsifications might have occurred over a period of ten years.
Aircraft maker Boeing said it was inspecting Kobe Steel products but said it had no reason to believe safety had been put at risk.
Speaking to reporters after visiting the ministry, Kawasaki said, "Possibly at the end of October, we'll announce our efforts to find the cause of the irregularities and our preventive measures".