Following proceedings opened by Swiss authorities against Blatter, as well as the questioning of Michel Platini, the head of European football governing body Uefa, Prince Ali bin al Hussein voiced his anger in a statement Saturday.
He said the suspicions of criminal mismanagement against Fifa's veteran leader highlighted "the need for new leadership that can restore the credibility of Fifa".
"We cannot change the past but we can have a future where Fifa member associations are able to focus on football rather than worrying about the next scandal or criminal investigation involving Fifa leadership," he said.
The prince, a former Fifa vice-president, who challenged Blatter in an election this year, said Fifa "has already changed, shaken to its very core by the scandals that have decimated our governing body and cast a cloud over the entire organisation."
After Blatter announced he would step down four days after his reelection on 30 May, the prince, South Korean tycoon Chung Mong-Joon, also a former Fifa vice-president, and Uefa's Michel Platini, are the leading candidates in the election to be held on 26 February.
Platini was questioned by the Swiss authorities on Friday afternoon.
They claim he received a payment of two million Swiss francs from Blatter three months before announcing he would not challenge Blatter for reelection during that year's race for the Fifa presidency.
"Concerning the payment that was made to me, I wish to state that this amount relates to work which I carried out under a contract with Fifa," Platini said. "I was pleased to have been able to clarify all matters relating to this with the authorities."