Blatter and Uefa chief Michel Platini read from the same script over 2011 payment.
A defiant Sepp Blatter insists he has done nothing wrong after Swiss authorities launched criminal proceedings against him.
The Fifa president said in a statement released via his lawyers that the controversial payment to Uefa President Michel Platini that initiated the probe was “valid compensation and nothing more”.
The statement added that Mr Blatter told staff in a meeting he will remain as president until February, when an election to choose his successor will be held.
The statement said: “President Blatter spoke to FIFA staff today and informed the staff that he was cooperating with the authorities, reiterated that he had done nothing illegal or improper and stated that he would remain as president of FIFA.>
“On the (UEFA President Michel) Platini matter, President Blatter on Friday shared with the Swiss authorities the fact that Mr. Platini had a valuable employment relationship with FIFA serving as an adviser to the president beginning in 1998.
“He explained to the prosecutors that the payments were valid compensation and nothing more and were properly accounted for within FIFA including the withholding of Social Security contributions.
“Because of the continuing investigation President Blatter will answer no further questions at this time.”
Mr Blatter is suspected of “criminal mismanagement or misappropriation” and his office has been searched.
The allegations relate to suspicion over a “disloyal payment” of 2m Swiss francs (£1.3m) to Mr Platini, who has been questioned as a witness.
The payment by Mr Blatter from Fifa funds was according to Blatter, for work carried out by his former ally between January 1999 and June 2002.
Mr Platini said the payment “relates to work which I carried out under a contract” and he “was pleased to have been able to clarify all matters” to the authorities.
On Monday he said the payment was fully declared to the authorities in accordance with Swiss law and that he has offered to give Fifa’s ethics committee any additional information.
TV rights deals sold to the now-disgraced former FIFA vice president Jack Warner are also part of the investigation into Mr Blatter.