Valcke's comments came on the day Brazilian organizers delivered the third of the six stadiums that will be used in the warm-up tournament, which begins on June 15.
"The next few weeks will be an acid test for the host cities, the local organizing committee, the federal government and FIFA on the final lap of preparations for the FIFA Confederations Cup," Valcke said in his latest column published on FIFA's website. "We are all working together tirelessly against the clock to make sure that the facilities will be ready to host a world-class tournament in two months."
After a series of delays, the Arena Fonte Nova was finally opened Friday in the northeastern city of Salvador, and Valcke said local organizers have promised to deliver the remaining three venues by the end of the month.
FIFA initially wanted all six stadiums to be ready last December, but was forced to extend the deadline because of constant delays in construction. Infrastructure work in the host cities will not be entirely done either, and Brazilian officials recently acknowledged that some of the promises made on telecommunications may not be completely fulfilled.
"We will make it," Valcke said. "It will be a fantastic tournament, but not all operational arrangements will be 100 per cent. It is impossible to expect this to happen in the shortened preparation time — in most cases, less than two months instead of the scheduled six — due to the compromises we made with the cities."
Local organizers had promised that all venues would be ready by April 15, but that deadline won't be fulfilled. The president of the local organizing committee, Jose Maria Marin, said last year that the stadiums not ready by that date would be excluded from the competition. But the venues in Brasilia, which will host the tournament's opener, and in Rio de Janeiro, home to the final at the Maracana, won't be ready by then.
FIFA said it will not tolerate these kinds of exceptions next year.
"I want to reiterate — this will be impossible to repeat for the FIFA World Cup," Valcke said. "(This) has been acknowledged by the federal government and LOC. The deadline for the FIFA World Cup stadiums delivery stands firm as December 2013. There will be no compromise."
He noted that getting the country ready for the World Cup "is an infinitely more complex and demanding job."
"In 2014 we expect more than half a million international visitors alone, and in total, more than three million spectators flocking to the 12 stadiums," Valcke said. "The scale and magnitude of the FIFA World Cup requires a minimum six month operational set-up.
"Whilst we are totally focused on the delivery of the FIFA Confederations Cup, we need to keep working full speed on the 2014 infrastructure in parallel."
Valcke said he will travel to Brazil in May to inspect construction at stadium in the northeastern city of Natal, and that FIFA President Sepp Blatter will visit all 12 World Cup host cities in June, during the Confederations Cup.
Nearly 550,000 tickets have already been sold for the warm-up tournament, "the best sales record to date in the history" of the tournament at this stage, according to FIFA.
Brazil, Spain, Italy, Mexico, Japan, Tahiti, Nigeria and Japan will participate in the tournament among continental champions. Brazil plays as host and Spain as the defending World Cup champion. Italy qualified as runner-up to Spain at the Euros.
The Confederations Cup will be played in Brasilia, Rio de Janeiro, Fortaleza, Salvador, Recife and Belo Horizonte.
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