During a two-week trip that ended Thursday, Valcke sent warnings to organizers in Natal, Porto Alegre and Sao Paulo, which will host the World Cup's opening match in two weeks. He said it was a "race against the clock" in Natal and there was a lot "yet to be done" in Porto Alegre.
In Sao Paulo, FIFA requested a second test event at the delayed Itaquerao Stadium that will host the Brazil-Croatia match on June 12. It is unlikely, however, that the venue will be tested at full capacity.
Valcke said he was pleased with the work underway in the other nine host cities, including Curitiba, which earlier this year was nearly excluded from the tournament because of chronic delays.
Valcke's final stop on yesterday was in the northeastern city of Salvador, where he said there was "no time to waste" but praised the commitment of local organizers to make sure everything will be ready in time.
"All must be perfect that day," Valcke said on Twitter.
"Pleased with Salvador's commitment to work with our on-site team to finalize remaining works for fans, media & teams.