Blatter was addressing delegates of the African and Asian confederations at their extraordinary congresses ahead of FIFA's annual congress which starts here on Tuesday.
The African congress, which declared its "continued support" for Blatter, who intends to run for a fifth term as president next year, also passed a resolution condemning what it called the British media's racist attack on its officials.
Blatter's comment came in the wake of a series of fresh allegations made by Sunday Times newspaper about the award of the Cup to Qatar and rumblings from sponsors who are unhappy with the current trouble FIFA is facing.
Blatter, without defining who "they" were, told Asian delegates "they want to destroy us; they don't want to destroy football, but they want to destroy the institution (FIFA)".
He got a standing ovation when he told the delegates to "show unity in FIFA".
Earlier on Monday, Blatter spoke to delegates at the African Congress and without naming names described attacks on the Qatar World Cup as "racist".
The Sunday Times over the last two weeks has published a series of articles expanding on allegations that the former president of the Asian Confederation, Mohamed Bin Hammam, had used money from secret slush funds to help win votes and support for the Qatari World Cup bid.
Qatar denies the allegations and says it was not connected to Bin Hammam.
Qatar was awarded the World Cup by the FIFA executive committee in December 2010, beating rival bids from the United States, Australia, Japan and South Korea.
However, the Sunday Times made new allegations that Bin Hammam specifically targeted African soccer officials and Issa Hayatou, the president of the African Confederation, to help create a groundswell of opinion in favour of the Qatari bid.
Blatter said: "Once again there is a sort of storm against FIFA relating to the Qatar World Cup. Sadly there's a great deal of discrimination and racism and this hurts me."
Hayatou, approached by Reuters in the lobby of Sao Paulo's Grand Hyatt Hotel after the congress, said: "I am very content with what president Blatter said. We support him, and I was very happy with what he told the delegates."
In the wake of the problems facing FIFA, five of FIFA's six major sponsors have expressed their displeasure over the situation.
Sportswear maker Adidas, which has been associated with FIFA since the 1950s, said in a statement on Sunday: "The negative tenor of the public debate around FIFA at the moment is neither good for football nor for FIFA and its partners."
Monday's developments coincided with Michael Garcia, the head of FIFA's investigatory chamber of their Ethics Committee, concluding his report on alleged corruption surrounding FIFA officials, which has taken him two years to complete.
He will submit the report to German judge Hans-Joachim Eckert, the head of the Ethics Committee's adjudicatory chamber, in around six weeks.
If he finds corruption, soccer officials say Qatar could be stripped of the Cup.
- Sports & Recreation
- Mohamed Bin Hammam
- Qatar World Cup