MEXICO CITY — Guatemala’s president, Otto Pérez Molina, angrily rejected calls for his resignation on Sunday, denying any involvement in a far-reaching scheme to defraud the government of customs revenue in exchange for bribes.

“I will not resign, and I will fully face and submit to the procedures that correspond to the law,” Mr. Pérez Molina said in a televised address.

The defiant statement came as he grew increasingly isolated after much of his cabinet resigned over the weekend and Guatemala’s most powerful business group demanded that Mr. Pérez Molina step down immediately.

The scheme, in which importers paid bribes to Tax Authority officials to obtain discounts on duties, has rocked Mr. Pérez Molina’s government and generated four months of mass demonstrations.