There have been no reports of any such accidents in the UK.
The investigation will look into allegations of momentary loss of braking power while travelling over uneven road surfaces.
As depressing the brakes further activated normal braking, Toyota said the glitch was not legally a safety hazard and said it had received no reports of any accidents related to it.
Mr Fonseca told the BBC that the braking problem was "not a defect, but a characteristic of the way the ABS system is tuned."
However, he did say that "we are very disappointed to have let customers down and accept that we could have handled [the problem] better."
On Thursday, the carmaker reported a net income of 153 billion yen ($1.68bn; £1.06bn) for the final three months of 2009, compared with a loss of 164 billion yen a year earlier.
The firm also said it still expected higher sales and to make a profit this year, despite the heavy blow to the company's reputation.
Toyota estimates its losses will reach $2bn (£1.23bn) in costs and lost sales from its worldwide recall of vehicles that might have faulty accelerator pedals, but a recall of Prius models would send this figure even higher.
"The losses could escalate if it turns out that the trust and reputation the company built up over a period of decades has been demolished almost overnight," said BBC business reporter Jorn Madslien.
Have you experienced similar problems with the accelerator of your Toyota? Have you been contacted by Toyota? You can get in touch with us using the form below:
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.