On Monday, the UCI said it was disbanding the Independent Commission investigating the Lance Armstrong drugs scandal in favour of a truth and reconciliation commission (TRC), a move which, it said, was supported by Fahey.
The WADA president angrily begged to differ on Tuesday.
"WADA is dismayed by the press release issued by UCI yesterday, both in terms of its content and its deceit," he wrote in a statement.
"Instead of any continuing professional dialogue with WADA's president, UCI has publicly announced by way of a press statement that WADA has agreed to work with it on some form of truth and reconciliation," the statement said.
"This is not only wrong in content and process, but again deceitful. The fact is that WADA was awaiting a reply to the correspondence when the UCI release was delivered."
UCI president Pat McQuaid said in Monday's statement that WADA had "no confidence in the existing Independent Commission process".
Fahey said: "WADA has never questioned the integrity and independence of the members of the commission, but solely the ability of the commission to work properly under the contract given by UCI to the commission."
Adding to the ridicule of the situation, the UCI issued a statement responding to WADA's response to Monday's statement.
"I am very saddened that it has come to this, but I cannot allow the latest blatant and aggressive misrepresentations contained in WADA's most recent press release to go unchallenged," McQuaid was quoted as saying in Tuesday's UCI statement.
"Mr Fahey is saying one thing in public and quite the opposite in correspondence with me."
Attached to the statement was a pdf of a letter from Fahey to McQuaid emailed to the UCI president by WADA general director David Howman.
In the letter, Fahey refers to the Independent Commission as "your so-called independent commission", saying it "might not be able to continue under new terms and procedures".
"There are concerns as to the flaws, that have already been pointed out, in the way this Commission has been established and set (or was given) its terms," Fahey continued.
"The major issue is the real question of independence, both real and perceived. This panel may have set its terms, but did not have the independence to change them when its own lawyers advised it to do so.
"I think it is already too compromised to remain credible and believe the process should start over from a new beginning.
"I appreciate that this may involve some extra expense, but the existing Commission can be requested to provide any information in its possession to the new Commission."
Two weeks ago, Fahey had accused the UCI of setting up a "useless" independent commission, while cycling's governing body was at the time ruling out the possibility of a truth and reconciliation process.
WADA and the UCI had already fallen out in 2006 over the UCI-commissioned Vrijman report that cleared Armstrong of any wrongdoing after sports daily L'Equipe had revealed that samples from the American from the 1999 Tour de France showed traces of EPO.
Armstrong was banned for life and lost his seven Tour titles last October after a report by the U.S. Anti-Doping Agency (USADA) showed the Texan had set up a sophisticated doping programme.
After more than a decade of denials, Armstrong admitted this month that most of his career had been built on a lie.
The Independent Commission expressed its regret after being disbanded by the UCI.
"The commission remains concerned as to WADA's and the UCI's ability to agree the scope, timing and structure of the TRC and also whether the T&R process is sufficiently advanced to justify the UCI's termination of this inquiry," it said in a statement.
"Neither the UCI nor interested stakeholders have provided sufficient co-operation to enable the commission to do its job. This failure to cooperate makes our task impossible."