Michael van Praag, head of the Dutch football association, said Blatter should quit when his term ends next year. A similar demand was made by David Gill, vice-chairman of England's Football Association,
Blatter, 78, officially opened FIFA's annual congress at a gala evening in Sao Paulo without mentioning the attacks or corruption controversy. He is expected to use the congress to announce on Wednesday that he will seek a new four year term.
"Tonight we are in a festive mood because let's say the discussions and all of what's linked with FIFA and is so important nowadays, we will discuss it tomorrow," Blatter said.
Van Praag challenged Blatter when he appeared before a closed meeting of the European confederation, UEFA. Some federations are angry because Blatter said in 2011 when he secured his latest term that it would be his last.
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"Mr Blatter, this is nothing personal but if you look at FIFA's reputation over the last seven or eight years, it is being linked to all kinds of corruption and all kinds of old boys' networks things," Van Praag said he had told Blatter.
Blatter replied that he would not resign straight away, according to the official.
The English FA's Gill also said it was "disappointing" that Blatter had changed his stance and the FIFA leader should leave next year.
"I think we need a full, frank and open debate about what FIFA needs going forward."
UEFA president Michel Platini has been touted as a possible rival to Blatter when the FIFA vote is held in May next year. Platini has said he will only decide his candidacy in September. Van Praag said that if Platini does not stand then UEFA should agree another candidate to stand against the Swiss official.