Mr Chung resigned on Friday after an audit by world football's governing body, FIFA, identified potential fraud in a multimillion-dollar project to build a new headquarters for the OFC in Auckland.
According to the New York Times, the audit found Mr Chung had hired, without issuing a tender, a company to construct the headquarters which had no experience of the work required.
Investigators were reported to have found close relationships between the companies advising the OFC on the project and those chosen to complete it.
A statement from the exceutive committee said it had analysed the audit, and that in light of the findings it had appointed an external lawyer to lead an internal investigation into potential wrongdoings and to take legal action, if required.
"A forensic audit has been ordered to review, in detail, the processes taken in relation to the OFC Home of Football and the financial processes adopted by the OFC Administration in past years," the statement said.
The executive pledged to co-operate with relevant authorities throughout the process. This included implementing all the conditions set out by the FIFA Audit and Compliance Committee as soon as possible.
Meanwhile, Sunday's meeting resulted in a decision that the OFC would be "led collegially" by the executive itself until its congress in June when a president is elected to replace Mr Chung.
The elected member will serve out the current term of OFC President, which concludes in 2019.
The OFC is to set up a reform committee to review its current constitution, policy and practice activity. According to the statement, this committee will be formalised at the OFC Congress in June.
Mr Chung, who is from Papua New Guinea, has also lost his position as FIFA senior vice president.