A Fifa statement confirmed a report in Swiss newspaper Blick, which said Blatter told a party: "I did not resign, I put myself and my office in the hands of the Fifa congress."
Blatter is thought to be considering standing for re-election as president.
Two criminal investigations into alleged Fifa corruption began in the week that Blatter was elected for a fifth term in charge.
Four days after being voted president, Blatter - who is reportedly under investigation in the United States - said: "While I have a mandate from the membership of Fifa, I do not feel that I have a mandate from the entire world of football.
"Therefore, I have decided to lay down my mandate at an extraordinary elective congress. I will continue to exercise my functions as Fifa president until that election."
However, Blatter did not use the words 'resign' or 'resignation'. He did add, however, the election would be for his "successor" and said: "I shall not be a candidate."
The Fifa statement added the quotes in Blick were "fully in line with the speech of the president on 2 June".
Labour MP Chris Bryant, the shadow secretary of state for culture, said: "Sepp Blatter's antics remind me not so much of the hokey-cokey as Glenn Close in Fatal Attraction.
"It's time Fifa put an end to all this speculation, which is harming the sport, and give a final date for Blatter's departure."
Meanwhile, Blatter may not attend the final of the Women's World Cup in Canada because of the twin investigations into Fifa by American and Swiss authorities.
He would normally present the trophy to the winning team, but Fifa will not confirm whether Blatter or secretary general Jerome Valcke will attend.
A Fifa spokesperson said: "In terms of the Fifa president and the Fifa secretary general, their future travel plans will be confirmed in due course."