Leoz said that while Africa and Asia had size and Europe had economic wealth, South America offered quality and an unmatched record at World Cups.
South America was given four automatic places at the 2002 World Cup, while fifth-placed Uruguay played off against Oceania winners Australia.
Soccer's world governing body FIFA, under pressure to increase places for Asia and provide a direct one for Oceania, has considered reducing the South American quota to four but Leoz wants more slots rather than less.
"We think it should be five," he told Reuters, seemingly bemused at the idea that South America could lose a place to Oceania after Uruguay beat Australia in last year's playoff.
"That's what I ask myself," he said.
Leoz remembered being involved in a heated argument last year with Issa Hayatou after the African Football Confederation (CAF) president suggested reducing the South American quota to three places.
Hayatou was running for FIFA president at the time.
"I had a very heated discussion with the African president. He wanted three for South America. I asked him why he was suggesting this.
"It was very unpleasant," Leoz said.
The 73-year-old Paraguayan, who has headed the CSF since 1986, pointed out that his continent had won more than half the World Cups, even though it could not hope to compete with Europe on economic terms.
"We have won nine of the 17 World Cups, Europe has won eight," he said.
"We have won more than 50 percent of the Intercontinental finals so we have supremacy at club and national team level."
Leoz added that although Real Madrid beat Paraguay's Olimpia in last week's meeting of European and South American champions in Japan, Brazilians Roberto Carlos and Ronaldo and Argentine Esteban Cambiasso were among the Spanish club's key players.
"Seventeen players (including the substitutes) on the pitch were South Americans," he said. "Quality is our business card.
"We have fewer inhabitants but we still have the raw material...There is always a South American distinguishing himself at the World Cup.
"We receive in television rights the same amount for one competition as UEFA receive for a match involving Real Madrid," he added.
"We have a very small market -- but good football."