In an email to AFP, FIFA confirmed the letter was authentic but said Valcke acted within his role, supporting FIFA's investigation.
"I am surprised by these comments. Frankly, this is a bit low," Valcke said in the email.
"The facts clearly show that I acted at the request of the deputy chairman of the ethics committee and perfectly in accordance with the FIFA code of ethics. Contrary to what these comments appear to insinuate, I never deviate from my line of duty."
Bin Hammam's suspension by FIFA over the bribery accusations led to his withdrawal from the world football body's leadership election, handing incumbent president Sepp Blatter a fourth consecutive term in office.
The controversy has highlighted allegations of corruption in FIFA and sparked calls for reform of its governance structure, which anti-graft watchdog Transparency International earlier this month called "opaque".
The vote-buying accusations also raised questions over last year's controversial decision to award Qatar the right to host the 2022 World Cup, beating Australia, the United States, South Korea and Japan.
Bin Hammam, a former chairman of the Qatar Football Association, had played a key role in pre-vote lobbying for his home country's bid.
PTI