The English FA asked other nations to support its call for a delay to allow a rival candidate to step forward, rather than allow Blatter, 75, to be re-elected unopposed for a fourth term.
The Scottish FA backed its English counterpart, but other national associations seemed less willing to throw their weight behind the Britons.
Transparency International also called for a postponement in a press release.
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”Free and fair elections cannot take place when there is a suspicion that voters may have been swayed. Two major figures in football politics have been suspended recently for alleged vote-buying. FIFA delegates know that they must clean house if their vote is to have legitimacy,” said Sylvia Schenk, a senior advisor on sport to the organisation.
Allegations of cash-for-votes in both the FIFA presidency campaign and the World Cup bidding process have left FIFA reeling. Blatter, a Swiss national who has run FIFA since 1998, is standing unopposed after rival Mohamed bin Hammam withdrew over bribery allegations.
"We call on FIFA and ask other national associations to support us with two initiatives," English FA chairman David Bernstein said in a statement.
"First, to postpone the election and give credibility to this process, so any alternative reforming candidate could have the opportunity to stand for President."
"Secondly, to appoint a genuinely independent external party to make recommendations regarding improved governance and compliance procedures and structures throughout the FIFA decision making processes for consideration by the full membership," he added.
The Guardian reported that a number of football sponsors also criticised the recent goings on at FIFA, including Adidas, Coca-Cola, and the airline Emirates.
LIMITED SUPPORT
The FA had already said it intended to abstain in the election for FIFA president.
England's relations with FIFA have been strained since it failed in a bid to host the 2018 World Cup despite a campaign which featured Prime Minister David Cameron and Prince William. FIFA awarded the competition to Russia last December.
The FIFA President is elected in the year following a World Cup by a Congress which is attended by all member associations.
The only way Blatter will not be re-elected on Wednesday is if the FIFA Congress proposes and passes a motion to call off the vote with the support of 75 percent of voting delegates.
The English move did not appear to have much momentum behind it. "We have not had a chance to sit down and discuss the matter with the English or even to read their statement," Kirsten Nematandani, president of the South African Football Association, told Reuters by phone from Zurich.
"Maybe they will still seek to engage with us before the Congress starts."
The head of the French Football Federation said he hoped the issue could be defused at Congress.
"All this certainly does not do any good to the world of football," Fernand Duchaussoy told reporters.
"I hope there will not be a clash at the Congress tomorrow, but you cannot rule it out."
(Additional reporting by Sonia Oxley, Mark Gleeson and Pascal Lietout; Editing by John Mehaffey and Ed Osmond)
