Wei's predecessor Nan Yong, his deputy Yang Yimin, the former head of refereeing and a marketing executive at the CFA were among more than 20 officials arrested or detained in the last two months on suspicion of match-fixing.
"I do not agree that the CFA are all liars ... The behaviour of those individuals does not represent the CFA," Wei told a news conference.
"The problem is that the CFA administrative system is far behind the development of professional football ... the match-fixing scandals are to some extent related to the system," he added.
"The ethics of football workers need to be strengthened. So far four CFA officials have been taken under judicial action or detention. It reflects an ethical problem in the CFA administration."
Wei said match-fixing was not the only problem that faced the CFA.
"The credibility of CFA was damaged by the decline of the national team and the scandals in the professional league," he said. "Our target is to profoundly improve the professional game in China and our work would then revive our credibility."
Wei said he had met Italian tyre maker Pirelli, which last year signed a three-season deal as title sponsor of the top flight Chinese Super League (CSL), and it had agreed to continue its backing.
"There is no problem of our sponsor quitting the CSL," he said.
NORMAL START
The CFA was planning for a normal start to the CSL season on March 20, he added, but the police investigation might disrupt those plans.
"Whether we can start on time is not our decision. It is beyond our authority," he said.
Wei, who was formerly in charge of water sports at the Chinese sports ministry and described himself as a "transitional figure", said punishments for clubs found guilty of match-fixing would await the conclusion of the police probe.
The Asian Football Confederation (AFC) earlier said it was monitoring the ongoing scandal in China.
"AFC has always taken a very strong stance against match-fixing," the continental governing body said in a statement. "This is a disease that needs to be cured with strict sanctions along with educational programmes.
"AFC will continue to monitor the situation in China and await the results of the investigation."
