Madrid asked Blatter on Tuesday to apologize for having mocked Ronaldo while praising Barcelona rival Lionel Messi at a recent event in England.
Blatter later complied, trying to downplay an incident that had pitted the sport's most powerful executive with its richest club and one of its biggest stars.
Blatter had told an audience at Oxford University that Ronaldo "is like a commander on the field of play" before strutting around the stage to the laughs of the students in attendance.
Madrid coach Carlo Ancelotti said early on Tuesday that club president Florentino Perez had sent a letter to Blatter asking him to "rectify what I consider a lack of respect for a serious and professional player."
Ronaldo took Blatter's stinging words, and mimicry, to heart.
"This video (of Blatter's comments) shows clearly the respect and consideration that FIFA has for me, for my club and my country," Ronaldo wrote on his Facebook page. "Much is explained now. I wish Mr. Blatter health and a long life, with the certainty that he will continue to witness, as he deserves, the successes of his favourite teams and players."
Blatter asked both Ronaldo and his club for forgiveness, sending a letter of his own back to Perez, which Madrid posted on its website.
"I want to clarify that for me Cristiano Ronaldo is at the same level as Messi and that they are both outstanding players, each in their own way," Blatter said in the letter.
Blatter said he was "sorry that this situation produced in a university event hurt as much and I apologize for it. It was never my intention to embarrass or disrespect to Real Madrid CF, or one of their players or their fans..."
While slighting Ronaldo during the public event, Blatter said he preferred Messi, the Argentina forward who has won FIFA's world player of the year award for the past four years.
Ronaldo won the award in 2008, finishing second in voting behind Messi in 2009, 2011 and 2012.
In his letter to Blatter, Perez said he was concerned that the FIFA president's deriding comments would hurt Ronaldo's chances at winning the sport's most prestigious individual award for a second time.
"We believe that your comments could condition the vote of those who will decide who will receive the award," Perez said in the letter, which was also posted on the club website.
The incident came on the day FIFA included Ronaldo and Messi on its list of 23 finalists for this year's world player of the year award. The list will be pared down to three players in early December.
While saying both Ronaldo and Messi were "extraordinary players," Blatter made it clear during his talk at Oxford that prefers what he sees as Messi's more subdued personality.
"Messi is a good boy, that every father and every mother would like to have at home," Blatter told the Oxford crowd. "He's a kind man, a good boy. That's what makes him so popular, and naturally he'll always get a lot of votes because he plays well and scores goals."
Then, while comparing Messi and Ronaldo, Blatter made a joke about Ronaldo's hair.
"They don't have the same attitude and that gives life to football. One has more expenses for the hairdresser than the other but that doesn't matter," Blatter said.
Ancelotti defended Ronaldo's character.
"I completely agree with the president (Perez)," Ancelotti said. "I haven't spoken to Ronaldo about this. I think he shows every day and in every match that he is a serious and professional player that respects everyone."
Ronaldo also received support in Portugal.
Portuguese football federation president Fernando Gomes said Ronaldo is "often misunderstood because he's forthright and honest," and that his frankness sometimes "gives rise to a negative image which isn't him."
The dispute is bound to strengthen the belief among some Madrid fans and sections of the Madrid-based sports media that FIFA has a bias for Barcelona and Messi.
Former Madrid coach Jose Mourinho snubbed FIFA's awards gala for the past two years while he was at the Spanish club, as did Ronaldo in 2012. Mourinho accused Barcelona of receiving help from FIFA referees in ousting Madrid from the 2011 Champions League semifinals.
AP sports writer Graham Dunbar in Geneva, Switzerland, and AP writer Barry Hatton in Lisbon, Portugal, contributed to this report.Suggest a correction