FIFA's director of communications Walter de Gregorio is to resign after making a joke on television about the scandal-hit football body, while pressure mounted for his boss Sepp Blatter to step aside at once.
The European Parliament said Blatter's failure to depart immediately would block efforts to rid FIFA of rampant corruption.
The FIFA president announced his resignation last week as US and Swiss authorities widened their investigations into bribery and corruption at the sport's global governing body, but he is still at his desk.
EU lawmakers heaped pressure on Blatter, 79, voting in favour of an eight-page resolution with a series of demands to clean up football.
The resolution -- non-binding but still indicative of public opinion in Europe -- welcomed Blatter's decision to resign, but expressed "serious concern" that he might stay on for a further nine months before a new leader is appointed.
The election to find a replacement for Blatter will take place in Zurich between December and February, FIFA announced, with the exact date decided at an executive committee meeting on July 20.
The soap opera at FIFA took another turn when it announced that De Gregorio was leaving two days after making a joke at FIFA's expense on a Swiss chat show.
The Swiss-Italian, who had taken up his role September 2011, had become a prominent figure within FIFA as a mouthpiece for the organisation, appearing in public debates and on television.
He had fronted up to the media storm two weeks ago in the immediate aftermath of a dawn raid on the luxury hotel when seven football officials, wanted by United States prosecutors on corruption charges, were arrested by Swiss police.
He also introduced the news conference where Blatter announced his resignation and appeared close to tears as the departing president announced his exit.
De Gregorio's departure follows an appearance on Swiss TV when, at the end of the programme, he was asked to tell his favourite joke.
He replied: "The FIFA president, secretary general and media director are sitting in a car. Who's driving. Answer? The police."
A FIFA statement gave no reason for De Gregorio leaving what had become an increasingly thankless job of defending FIFA during the scandal.
"Walter has worked incredibly hard for the past four years and we are immensely grateful for all he has done," said FIFA Secretary General Jerome Valcke.
The race to succeed Blatter gathered a new challenger on Wednesday when football great Zico formally declared his candidacy for the FIFA presidency, but the Brazilian admitted his chances of success were limited.
Under FIFA rules he needs the backing of five countries affiliated to world football's governing body, which he does not yet have, while he said UEFA boss Michel Platini had advised him to run for head of the Brazilian Football Confederation instead.
The rules governing how the FIFA president is elected have come under the spotlight since the corruption scandal erupted, but any plans to alter the voting system are likely to meet stiff opposition.
Football chiefs in Asia, Africa, Latin America and the Caribbean voiced concerns on Thursday at German proposals to change the one member one vote system and hand a greater influence to more established football power-houses.
The current system has been widely credited with providing Blatter with his power base as he ruled FIFA for 17 years, aided by votes from less prominent football nations that received development funds aimed at promoting the sport.
"If tomorrow one member association is going to be more equal than the other, then of course that is going to raise serious issues, and that would not be good for world football and that would not be good for FIFA," Pakistani football chief Faisal Saleh Hayat told Reuters.
Zimbabwe Football Association spokesman Xolisani Gwesela said it would be unfair for countries in Africa and the developing world not to have the same vote as Germany or England.
Raymond Tim Kee, head of the Trinidad and Tobago Football Federation, also opposed the German plan, saying: "Big nations will trample on small countries like us in the Caribbean."
Jacinto Reyes, President of the Nicaragua Football Federation, added: "I am totally against this attitude because we have always spoken about racial discrimination and this idea is also discrimination."
As the corruption scandal widened, Paraguay's congress approved a measure withdrawing immunity from the headquarters of South America's CONMEBOL football confederation.