TOKYO, June 4 (Reuters) - Officials from Japan's transport ministry launched an on-site investigation at Toyota Motor's headquarters on Tuesday after irregularities were found in its applications to certify certain models.

The widening fallout over vehicle certification tests stem from a safety test scandal at Toyota's Daihatsu compact car unit and has spread to other Japanese automakers.

But Toyota, which has long prided itself on its reputation for safety and reliability, was the only automaker to undergo an on-site inspection.

Japan's transport ministry had announced plans to carry out the inspection a day earlier, when it said Toyota, Mazda , Honda, Suzuki and Yamaha Motor were found to have submitted either flawed or manipulated data when applying for certification of vehicles.

Toyota chairman Akio Toyoda, the grandson of the automaker's founder, apologised to shareholders, car fans and other stakeholders at a press conference on Monday.

"From a compliance standpoint, we think further strengthening of governance will be needed going forward," analysts at Goldman Sachs wrote in a note to clients.

Toyota's shares were down 1.1% on Tuesday morning, extending Monday's 1.8% loss. Those of Honda dropped 2.3%. Suzuki's and Mazda's shares both rose 0.9%.

Toyota and Mazda said on Monday they had both halted shipments of some models.

(Reporting by Daniel Leussink and Maki Shiraki; Editing by David Dolan and Edwina Gibbs)