Flanked by football great Pelé, who urged Brazilian fans to stand unified behind their still evolving national team, Valcke unveiled a clock in Rio de Janeiro counting down the days until the World Cup starts.
Valcke said that 12 months is enough time to finish work at airport terminals and the 12 stadiums that will play host to the event.
Aldo Rebelo, Brazil's sports minister, has said repeatedly that the stadiums will be completed by a December deadline.
"That is going to happen," Valcke said on Wednesday, echoing the comments by Rebelo, who was also at the unveiling of the clock.
"There is no Plan B. There is no solution other than having those 12 stadiums," Valcke added.
Six of the stadiums, including in Rio, Brasília, Belo Horizonte and three cities in Brazil's north-east, are mostly completed and are gearing up for the two-week Confederations Cup.
The smaller tournament, an eight-team competition that starts on Saturday, will serve as a World Cup warm-up and will help organisers test facilities ahead of the marquee event.
Pelé urged Brazil fans, known for booing the national team for anything other than outright dominance on the field, to be patient.
The three-times World Cup winner said the team's play is still a work in progress because the squad is predominantly made up of younger players including Neymar, the forward who recently joined Barcelona from Pele's former club Santos.
"Barcelona is the best collective team in recent memory," Pelé said. "This full year that he spends with Barcelona will be great training before coming back to the national team."
