He had already admitted the ticketing system, based on internet sales, was not suitable for South Africa, where the poor black population who are the country's biggest football fans do not have access either to the Web or bank accounts.
Last month, organisers belatedly introduced over-the-counter cash sales which unleashed a rush for tickets and significantly pumped up excitement over the tournament in the host nation.
"I have already said that the system we have put in place was not perfect for South Africa and for Africa," Valcke told a press lunch.
"For Brazil we say that we have to rethink and we will work on all the ticketing policies from scratch for 2014 because I agree that it could be that we are facing the same kind of situation in Brazil as in South Africa."
South Africa's Tourism Minister Marthinus van Schalkwyk earlier this week called the internet ticketing system a "huge mistake" for Africa. He also said ticket prices were too high.
Valcke acknowledged it was disappointing so few fans from other parts of the continent would be coming to the first African World Cup, estimating the number at about 40,000 out of 2.86 million seats available.
Asked about the arrest of a Saudi al-Qaeda member in Iraq who was allegedly plotting to attack the World Cup, Valcke said no warning had been received of any serious potential terrorist threat to the tournament.
SECURITY COOPERATION
He dismissed local reports that FIFA and foreign intelligence services were worried about South Africa's capacity to deal with such threats.
"It is clear for the time being that we have not received any threat on the World Cup, a real one, coming from one of the security agencies we are working with," he said.
Valcke said less than 200,000 tickets remained unsold and FIFA hoped to reach sales of 95 percent but three smaller venues - Polokwane, Nelspruit and Port Elizabeth - were cause for concern, with fears many seats would be empty.
In a bid to avoid this, FIFA was organising up to 200 free buses to bring people from borders with surrounding countries, including Zimbabwe which is close to Nelspruit and Polokwane. But he feared it was too late to attract extra fans this way.
To encourage more fans, FIFA has also extended the special cheap $20 category 4 tickets, originally available only to South Africans, to neighbouring countries.
Valcke said there was concern particularly about the Paraguay-New Zealand group stage match in Polokwane on June 24 and South Korea-Greece in Port Elizabeth on June 12.
Critics have attacked the building of expensive new stadiums in all three cities, saying they will be white elephants after the World Cup with no local football or rugby teams.
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