"Here the illness is not admitted to so you cannot cure the patient," the LFP's Javier Tebas was quoted as saying in Marca sports daily.
"There are institutions which are not aware of what goes on," he said.
"There is match-fixing and illegal betting. In a small percentage but there is also corruption in Spain."
An inquiry by European police forces, the European anti-crime agency Europol, and national prosecutors has uncovered about 680 suspicious matches allegedly fixed as part of a global betting scam run from Singapore.
They included qualifying games for the World Cup, the European Championship and the Champions League.
The matches in question, some of which have already been subject to successful criminal prosecutions, took place between 2008 and 2011, investigators said.
About 380 were played in Europe, and a further 300 were identified in Africa, Asia, and Latin America.
Tebas told Spanish radio last month the LFP was aware that some matches in Spain were being fixed.
"We are trying to unmask the cheats, because there are cheats in Spanish football," he said.
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