Blatter had personally said sorry to the Brazilian government for the affair on Tuesday, one day after Valcke had been similarly contrite.
FIFA have for months expressed concern in varying degrees over the extent to which preparations - renovation or construction of stadiums, as well as infrastructure projects - are on track for the first World Cup in Brazil since 1950.
Valcke said he profoundly regretted that an incorrect interpretation of his comments had triggered such an angry response from the host country.
"I would like to present my apologies to everyone who was offended by my comments,'' said Valcke, a French national.
He explained that in French, the phrase "se donner un coup de pied aux fesses'' (to give someone a kick up the backside) only meant "to pick up the pace''. The translation into Portuguese used a stronger expression, he added.
"I don't understand why things are not moving. The stadiums are not on schedule anymore and why are a lot of things late?'' Valcke had said last Friday.