Walter De Gregorio has left his post as Fifa’s head of communications days after making a joke on television about the world governing body, despite having defended it and been its most prominent public face throughout the recent crisis which led the president, Sepp Blatter, to announce his resignation although he currently remains at the helm.

Appearing on Swiss TV on Monday De Gregorio said: “The Fifa president, secretary general and communications director are in a car. Who’s driving? The police.”

A statement from Fifa said De Gregorio had decided to step down with immediate effect. It marks the latest twist in the crisis engulfing Fifa, which began two and a half weeks ago when the FBI and Swiss authorities arrested numerous officials following a dawn raid in Zurich amid allegations of endemic corruption.

Fifa confirmed on Thursday that the extraordinary executive committee meeting to decide the date for the presidential election will take place on 20 July in Zurich, with a statement saying the extraordinary elective congress will be held between December and February.

De Gregorio was present at Blatter’s resignation speech before a sparse media contingent. The Swiss has been one of Blatter’s most senior aides since joining Fifa in September 2011, and strongly defended it after the arrests.

Only hours after US and Swiss officials raided the Baur au Lac hotel in Zurich – amid the news that several senior Fifa officials faced extradition to the US on federal corruption charges – De Gregorio attempted to quell the growing storm at a press conference by describing the incident as good for Fifa.

He said: “This for Fifa is good. It is not good in terms of image or reputation but in terms of cleaning up, this is good. It is not a nice day but it is also a good day. The process goes on and we are looking forward.”

However, De Gregorio’s joke on Swiss TV appears to have proved pivotal for the former journalist, with Fifa releasing a statement on Thursday which said: “Walter De Gregorio has decided to relinquish his office with immediate effect as director of communications and public affairs. Mr De Gregorio joined Fifa on 14 September 2011 and will serve Fifa on a consultancy basis until the end of this year. His deputy Nicolas Maingot will resume the role ad interim.”

The Fifa general secretary, Jérôme Valcke – who has come under pressure for his involvement regarding a $10m payment made by Fifa in relation to the 2010 South Africa World Cup – said: “Walter has worked incredibly hard for the past four years and we are immensely grateful for all he has done. I am glad we will be able to continue to draw on his expertise until the end of the year.”

Walter De Gregorio’s joke on Swiss TV

The FBI said last week it was extending its investigation into corruption at Fifa into the bidding for the 2018 and 2022 World Cups, to be held in Russia and Qatar. The head of the organising committee for Russia 2018, Alexei Sorokin, stated that neither the US nor Swiss investigators had contacted Russia and criticised the “hysteria” surrounding Fifa’s current plight.

“We just need to ponder in whose interest it is to draw up the bridge between us and our partners in Fifa,” Sorokin said. “Strangely this comes when a sizeable Fifa delegation is in Samara, where we’re trying to prepare the World Cup together. It’s not necessary to put yourselves into some sort of hysteria or trance about all this. The organisation has the capability to self-regulate and possibly fix incorrect decisions made in the past. The participation of law enforcement organs isn’t necessary.”

On Thursday the European parliament called on Blatter to stand down with immediate effect, urging its member states to cooperate fully with the ongoing investigations into corruption.

Only two hours after De Gregorio’s departure was announced, an extract from the Fifa Weekly magazine was publicised in which Blatter wrote: “Fifa is going through difficult times. This makes me all the more proud that our organisation runs smoothly in a crisis.” It is thought he was referring to the Women’s and Under-20 World Cups when describing the smooth running of Fifa.