Swiss authorities have removed computer data from FIFA that a source said included records from the office of its President Sepp Blatter.
The FBI is investigating bribery and corruption at football's world governing body, including scrutiny of how the association awarded World Cup hosting rights to Russia, which won the bidding for 2018, and Qatar, which is due to host the finals in 2022.
Swiss authorities are conducting their own probe into suspected mismanagement and money laundering in connection with the award of the two tournaments.
A spokesperson for Switzerland's Office of the Attorney General confirmed "FIFA handed over today seized IT data to the OAG.
"As already communicated, the OAG has opened criminal proceedings against persons unknown," the spokesperson added.
A source close to the Swiss investigation said records from Mr Blatter's office were part of the probe.
It has also been reported data was also taken from the offices of Mr Valcke and FIFA's head of finance.
The OAG, which took data and documents from FIFA last month, will speak with Mr Blatter and other officials if they are of interest to its investigation.
FIFA confirmed it had handed over the data.
Defending himself Mr Valcke asked: "You want me to take this pen and to hit my head and say 'Hey! I have been stupid, I should have asked many more questions?
"You have decided that after Blatter, I have to be next head to be cut?" Mr Valcke said at a news conference in the Russian city of Samara, one of the 2018 host venues.
Meanwhile, FIFA has announced it has postponed the bidding for the right to host the 2026 World.
Mr Valcke said it would be "nonsense" to start the bidding process for the 2026 tournament for the time being.
Mr Blatter tendered his resignation as president on 2 June, four days after having been re-elected for a fifth term.
FIFA has begun the process of finding a replacement, saying its executive committee would meet in July to discuss dates for the Congress, which will elect a new president.
