Sao Paulo will be ready at "last minute" -- FIFA
View of the Arena Corinthians stadium, on April 22, 2014 in Sao Paulo - by Nelson Almeida
The stadium has suffered delays following two fatal accidents which left three workers dead, but Valcke said he was confident preparations were advancing well.
"Sao Paulo will be ready for the opening match," between Brazil and Croatia," said Valcke, adding there was "no choice" while repeating his mantra that "we cannot waste a single minute."
Valcke told reporters: "We are running against time, but yes, the stadium will host the opening game and, yes, we will organize the opening game and all the other games in this stadium.
He had earlier tweeted: "(The) next important event for us will be on 17 or 18 May when the first official test with full capacity will take place at Arena de Sao Paulo," Valcke tweeted.
With FIFA normally wanting three tests at venues Valcke indicated that Sao Paulo therefore faced "a very tight schedule" through to the June 12 kick-off.
He insisted he was "happy with progress" as "TV area & IT installations (are) taking shape, accreditation & volunteer centres open in 3 weeks."
FIFA set an initial deadline of December 31 for all 12 venues to be ready.
Sao Paulo was then put back to January 15 but delays have continued to dog the project.
Fatal accidents at the venues of Brasilia and Manaus killed another four workers while other delays have beset Porto Alegre, Cuiaba and Curitiba.
Valcke started off his latest monthly trip to Brazil by visiting Sao Paulo's Corinthians Arena, which he called a "beautiful football arena", ahead of trips to Curitiba, Cuiaba and Fortaleza through to Thursday.
Constructors symbolically handed over the Sao Paulo stadium, still unfinished, to owners Corinthians club last week ahead of expected delivered to FIFA on May 20.
Valcke was later due in the southern city of Curitiba to inspect the Baixada Arena, which he threatened to leave off the venue list until February sparing it following a ramping up of work there.
Wednesday will see Valcke in the central city of Cuiaba, whose stadium is also unfinished, before he heads down to Porto Alegre, where the stadium is ready save for temporary structures.
In Fortaleza on Thursday, Valcke is scheduled to visit the Aterro de Iracema site, which is due to host the Fan Fest, or open air street party area for ticketless fans.
"We are working with Brazil to make the 2014 #World Cup a successful reality," said Valcke, who Friday will attend a local organizing commitee meeting in Rio.
"We owe this to the 2.7m fans who have bought tickets to date."