FIFA responded by announcing that its executive committee will meet on July 20 in Zurich to decide when from December to February the election to decide Blatter's successor should be held.
That meeting will also discuss how to reform FIFA after American and Swiss corruption investigations unleashed turmoil on the organization two weeks ago.
The latest upheaval saw communications director Walter De Gregorio, closely tied to the embattled president since 2011, abruptly exiting FIFA three days after telling a joke about soccer's governing body on a TV talk show.
Still, Blatter praised FIFA's handling of the ongoing corruption crisis in the organization's in-house magazine.
"FIFA is going through difficult times," Blatter said in an excerpt of his column released on Thursday. "This makes me all the more proud that our organization runs smoothly in a crisis."
Blatter appeared to be referring to the smooth-running Under-20 and Women's World Cups in New Zealand and Canada. However, in what seemed like strange timing, the advance extract from Blatter's weekly column in a FIFA online magazine was released two hours after De Gregorio's exit was announced.
On Monday, De Gregorio was a guest of host Roger Schawinski on German-language station SRF. Schawinski closed the show by asking the former sports and politics journalist to tell his favourite joke about FIFA.
De Gregorio set up the punchline by saying the FIFA president, himself and secretary general Jerome Valcke were in a car, so who was driving?
After a pause for the host to comment, De Gregorio gave the answer: "The police."
Earlier, lawmakers from 28 European nations meeting in Strasbourg, France, voted on a resolution calling for Blatter to speed up his announced resignation and let FIFA appoint an interim leader.
"FIFA is perplexed by the European Parliament's resolution," said the Zurich-based soccer body which is not obliged to heed the parliament and previously dismissed criticism by lawmaker groups, including the Council of Europe.
Blatter is a target of the American investigation of corruption in soccer, and Swiss prosecutors are leading a separate probe into the 2018 and 2022 World Cup bidding contests.
If Blatter left before the election, FIFA rules require senior vice-president Issa Hayatou of Cameroon to step up as interim president.
Hayatou was reprimanded in 2011 by the International Olympic Committee for taking cash payments in the 1990s from FIFA's then-World Cup marketing agency. He also steered through two changes of CAF presidential election rules in the past two years to protect his position.
Hayatou is among 10 past and current FIFA executive committee members who Swiss authorities want to question in their probe of possible financial wrongdoing in World Cup bidding contests won by Russia and Qatar, respectively.
On Thursday, the European Parliament urged its member states — which do not include Switzerland — to "co-operate fully with all ongoing and future investigations on corrupt practices within FIFA."
However, Russia is not a member of the European Union, and its President Vladimir Putin has criticized American authorities for meddling in FIFA's affairs and seeking to have his country stripped of World Cup hosting.
Russia and Qatar have consistently denied wrongdoing. A FIFA investigation concluded last year that unethical behaviour by most of the nine bid candidates did not affect the outcome of votes by FIFA's executive committee.
Those December 2010 votes were the starting point of FIFA's current crisis, Blatter suggested last month. He blamed American justice officials and media in England, noting that both countries were losing World Cup candidates.
De Gregorio defended FIFA at a May 27 news conference called hours after the governing body's headquarters were raided by Swiss police, and seven soccer officials were arrested at a luxury Zurich hotel.
Then, the Swiss spokesman said it had been "a good day" for FIFA, which he said was committed to fighting corruption.
De Gregorio joined FIFA after working on Blatter's campaign team during the 2011 presidential election. FIFA said De Gregorio "would be retained as a consultant until the end of the year."
Valcke said in the FIFA statement that he was glad "we will be able to continue to draw on (De Gregorio's) expertise until the end of the year."
De Gregorio's deputy, Nicolas Maingot, will step up to the director's position.