The world and European champions have lost their last two matches and are without a win in three and surrendered top spot in La Liga to arch rivals Barcelona last weekend after a 1-0 reverse at Athletic Bilbao.
They followed up with a 4-3 Champions League defeat at home to Schalke 04 on Tuesday, squeaking through to the quarter-finals 5-4 on aggregate, and were roundly whistled by angry fans at the Bernabeu.
Barca host Real for the La Liga 'Clasico' on March 22 and Spanish sports daily Marca reported on Thursday that a humbling loss at the Nou Camp would prompt Perez to sack Ancelotti, who has a contract until the end of next season.
"To use the fact that we are not on our best form at the moment to report information that is not true is unacceptable," Perez told reporters.
"I want to state categorically that the club has full confidence in our coach and in our players," he added.
"And I want to say, contrary to a report published today, that whatever happens in the coming days and weeks Carlo Ancelotti will remain the coach of Real Madrid.
"We have the best coach and the best players that Real Madrid could have.
"As president of Real Madrid, I appeal to our fans to support our coach and our players and ask that they feel proud of them for all they have given us and for all they will continue to give us."
Perez also expressed support for Real's Wales winger Gareth Bale and goalkeeper Iker Casillas, who are struggling for form and have been the main targets of fan ire.
"Gareth Bale is one of the best players in the world," Perez, who set a transfer record when he bought Bale from Tottenham Hotspur for around 100 million euros ($106 million) in 2013, told reporters.
"The biggest clubs fought and continue to fight to secure his services.
"The only thing I can say is that we shouldn’t forget what he was able to achieve in his first year at Real Madrid."
Real host Levante in La Liga on Sunday before travelling to Barcelona for the 'Clasico' a week later.
($1 = 0.9403 euros)
(Reporting by Iain Rogers, editing by Toby Davis)
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