FIFA frets over Maracana refurbishment
Valcke visited the Arena do Copa outside Recife but said the famous Maracana, which he is due to visit Thursday, was preying on his mind.
"The city I'm travelling to in two days' is the one which is causing FIFA the most concern," he told reporters.
FIFA has said the six stadiums which will host matches in the Confederations Cup, considered a dress rehearsal for the 2014 World Cup, must be ready by mid-April.
"The date of completion is very important so we can test them before the start," Valcke said. "May is too late and that could cause a lot of trouble for FIFA, for the World Cup and for Brazil."
The Maracana, built for the 1950 World Cup and remodelled several times since, was due for completion in December but the deadline was put back to February and then April.
The latest rebuilding work started in 2010 at a cost of 900 million Reais ($457 million).
It is due to re-open with a friendly between Brazil and England on June 2.
Brazilian Football Confederation (CBF) technical director Virgilio Elisio said on Monday he was worried and that work would have to speed up.
The Recife stadium, previously one of the major headaches and which was less than half complete when the local organising committee visited for the first time last year, is 90 per cent ready, officials said.
"Now we have to work on the pitch, which is the most important project," said Valcke. "The pitch will be planted in the new few weeks but we don't have much tie for it to be ready.
"It's important that they have the same conditions for all the matches, that is something we try to guarantee," he said.