Football Association chairman Greg Dyke has insisted: "Sepp Blatter has to go as FIFA president."
Dyke's comments came after FIFA endured the darkest day in its scandal-strewn history as US investigators blew the lid on "rampant, systemic, and deep-rooted" corruption.
Dyke said: "Blatter has put out a statement saying now is the time to start rebuilding the trust in FIFA. There is no way of rebuilding trust in FIFA while Sepp Blatter is still there.
"Sepp Blatter has to go. He either has to go through a resignation, or he has to be out-voted or we have to find a third way.
"I think the time has come where the damage this has done to FIFA is so great that it can't be rebuilt while Blatter is there so UEFA has got to try to force him out."
Football's world governing body was plunged into crisis after a wave of arrests of football officials including two FIFA vice-presidents in Zurich on Wednesday on bribery, fraud and money laundering charges following an FBI investigation.
The US Department of Justice indictment of 18 people said bribes totalling more than 150million US dollars (£98million) had been paid for television rights, sponsorship deals and World Cup votes. The crisis led UEFA to call for Friday's FIFA presidential election to be postponed and the European body questioned whether its 53 voting associations should even attend the Congress.
In a separate development, the Swiss attorney general also opened criminal proceedings over the awarding of the 2018 and 2022 World Cups, seized documents and electronic data from FIFA's headquarters and will question 10 current FIFA executive committee members who voted on that tournament.
UEFA's statement has intensified the pressure on Blatter, but the world governing body has insisted the election will take place as planned.
The arrests began at 6am as Swiss police swooped on the five-star hotel used by FIFA executives and arrested seven officials including Jeffrey Webb, a FIFA vice-president from the Cayman Islands who holds a British passport. Another FIFA vice-president, Eugenio Figueredo from Uruguay, was also arrested and Swiss officials said six of the seven are contesting extradition proceedings to the USA to answer indictments.
US Attorney General Loretta Lynch said: "The indictment alleges corruption that is rampant, systemic, and deep-rooted both abroad and in the US.
"It spans at least two generations of soccer officials who, as alleged, abused their positions of trust to acquire millions of dollars in bribes and kickbacks."
The indictments implicate South Africa in paying 10million US dollars to disgraced former FIFA vice-president Jack Warner from Trinidad for votes to host the 2010 World Cup - with the money being channelled through a FIFA bank account authorised by an unnamed high-ranking FIFA official.
It also alleges corruption and bribery extended to the 2011 FIFA presidential election, and to agreements regarding sponsorship of the Brazilian national team by a major US sportswear company. Nike has sponsored Brazil since 1996 and said it opposes bribery and is co-operating with the authorities.
A warrant was issued for Warner's arrest in Trinidad and he is facing an extradition hearing to the USA. His two sons have pleaded guilty to corruption charges, while Chuck Blazer, who is believed to have provided much of the evidence to the FBI, has admitted 10 charges.
Warner later handed himself into authorities in Trinidad and was released on 2.5million US dollars bail pending an extradition hearing, according to a statement from Trinidad's attorney general.
FIFA reacted by provisionally suspending the 11 football officials among the 18 people indicted. Blatter issued a statement saying: "This is a difficult time for football, the fans and for FIFA as an organisation. We understand the disappointment that many have expressed and I know the events of today will impact the way in which many people view us.
"As unfortunate as these events are, it should be clear that we welcome the actions and the investigations by the US and Swiss authorities and believe that it will help to reinforce measures that FIFA has already taken to root out any wrongdoing in football."
Russia 2018 organising committee head Alexey Sorokin insisted he was not concerned about the criminal investigation into the awarding of the 2018 and 2022 World Cups and said there was no point in even discussing the idea of a re-vote for the tournaments - something FIFA has also ruled out.
He told Sky Sports News: "We have repeatedly stated that we're not afraid of any investigation.
"We cooperated with the investigation that was going on for about two years which was headed by Mr (Michael) Garcia. We submitted all the facts, all the papers, we submitted our testimonies - we did everything the process wanted us to do. We don't know what else we can contribute to that.
"We repeatedly said the process was transparent and that we're not concerned with any investigations. It's just strange there's a chance to go through the same thing again, where everything was seemingly closed."
Asked if he was worried about a re-vote, he added: "No, because we are so deep in the preparation, we've done so much. Our government, our country, has done so much already for the preparation of an excellent World Cup, I don't even want to discuss it with anyone."
On Blatter's future, he said: "We wish the current president all the success in the elections."
FIFA's chief medical officer Jiri Dvorak said Blatter sent his apologies at being unable to attend the medical conference.
Dvorak told delegates: "President Blatter apologises for not being able to come today because of the turbulence you have probably followed in the media.
"He said he has to fulfil his duties in the management of the situation which is probably more important than to come to us, so he sends his sincere apologies."