"I am not going to resign," the 79-year-old Perez told a press conference towards the end of a season in which Real Madrid will finish trophyless.
Barcelona defeated Real Madrid 2-0 in the Clasico at Camp Nou on Sunday to claim back-to-back LaLiga titles with three games to spare.
Madrid bowed out of the Champions League with a quarter-final exit against Bayern Munich.
Current Real coach Alvaro Arbeloa, who replaced Xabi Alonso in January, is unlikely to remain at the helm next season, and former Madrid coach Jose Mourinho has been linked with a potential return.
This season has seen Madrid finish without a major trophy for a second year running.
Fans have been protesting against star player Kylian Mbappe for a perceived lack of commitment, while there are stories of multiple training ground bust-ups, including one that sent midfielder Fede Valverde to hospital.
Perez justified his bid for a new term in response to what he dubbed an "absurd campaign" against Real Madrid.
"I've made this decision because an absurd situation has been created to generate a tide of opinion against the interests of Real Madrid," argued Perez.
"I've been here 26 years, and it’s been a wonderful time."
Perez took aim at media campaigns and other personalities, claiming they were taking advantage of this season's poor results to target him personally.
"I want to put an end to this anti-Madrid current that wants to destroy Real Madrid," he said.
"I'm standing for re-election to return the club's assets to its members.
"If anyone wants to run, they shouldn't just pretend - let them run, but let them say what they're going to do, how they're going to finance everything."