"It is completely false that there was an ultimatum or anything like that," Perez said during a news conference Thursday. "I am here to deny false information that has the objective of destabilizing the most prestigious institution in the world."
Perez called the conference to deny reports in Marca, the Spanish daily, that during a dinner held last week Casillas and Ramos asked for Mourinho to be let go at the end of the season and issued an "either he goes or we go" ultimatum to Perez.
Casillas and Ramos denied the published reports via press release Thursday.
"We categorically reject the use of our names and those of the rest of the team to publish information that we qualify as totally false," the press release said. "We would like to show our support to the figure of our coach, Jose Mourinho, to whom we owe our maximum respect."
Perez also denied the claims.
"There were four of us in the meeting," Perez said. "The only reason for the meal was to work out the bonuses for the current season. The meeting had a magnificent climate. What is published is not correct.
"I accept that some criticism can take place, although that seems to me unjust, but there are ethical limits which everyone must respect," he said.
"What was published is very serious and is a lie," said Perez. "I want to remind you that the unity of the fans and team members is what has made us the best club in the world."
Perez did not confirm or deny whether the players were weary of Mourinho's style of coaching. He said that although he rarely speaks on coaching matters, he felt compelled to call the news conference.
"When I woke up and saw this news it was so serious that if forced me to come here," he said. "When the line of ethics is crossed I will be here to defend the institution."
Perez said he had not spoken with Mourinho on Thursday.
"The grade of responsibility of the captains is incompatible with the published information," Perez said. "You can speak with the four people. I am speaking in the name of the club and its players."
The Spanish dailies have reported problems in the Real Madrid dressing room for the past weeks, including speculation over Mourinho's decision to drop Casillas from the starting goalkeeper's job in favor of Antonio Adan.