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WADA and the International Cycling Union (UCI) have been at loggerheads over how to proceed since a damning US Anti-Doping Agency (USADA) dossier led to the Texan rider being stripped of his record seven Tour de France titles for drugs offences.
Fahey told a London news conference on Tuesday that he had received a letter from the UCI late Monday suggesting the creation of a new inquiry to include four UCI members but not the governing body's president, Pat McQuaid.
The UCI, facing questions about how Armstrong was able to dope undetected for so long and alleged complicity, recently shut down its own independent commission over its role in the case, saying it preferred a "truth and reconciliation" process.
But a scathing Fahey said talk of "truth and reconciliation" was just "fancy words" that should be "left where they had some meaning in (post-apartheid) South Africa".
The blunt-speaking Australian added: "Cycling has a problem, a crisis of confidence. Only cycling can heal the problems cycling has... How long will the members (of the UCI) allow cycling to lurch from one crisis to another?
"It is not WADA's job to sort out the doping problems that may exist within a certain sport - that is the responsibility of the sport.
"WADA is here to help and to offer expert advice but it is not mandated to cure the doping ills that have been allowed to build up within individual sports over the last decades."
Fahey said the USADA inquiry had shown blood and urine tests were not the only way to catch dope cheats, adding that detailed corroboration of witness statements and testimony from fellow riders were a major weapon in the fight against drugs in sport.
But Fahey, who steps down at the end of his maximum six-year term as president later this year, said the prime responsibility for the Armstrong affair remained with the cyclist himself.
"It is not an excuse to say that other riders were doping and therefore I also had to cheat. It is not an excuse to say that riders in the Tour de France have been seeking an edge ever since the race was founded 100 years ago," he told reporters.
"The reality is that Mr Armstrong cheated for more than a decade, bullied others into cheating, bullied those who would dare to expose his cheating, and to this day continues to manipulate the facts for his own benefit."
Fahey also called for governments to stiffen national laws in the fight against performance-enhancing drugs.
Their use extended beyond the realm of elite competition to criminality, as highlighted by the recent Australian Crime Commission report into links between organised crime and drugs in sport, he explained.
"We hear about students using some form of drug as a study aid and members of the security services using steroids to increase their physicality to get stronger and supposedly less vulnerable," he said.
"We need for governments around the world to accept that doping is a societal problem. There needs to be legislation in place that enables effective mechanisms to identify doping and effective mechanisms to deal with them."
Sports officials had to do more, he said, adding: "Sport too needs to stop procrastinating and to make a real stand against this continuing trend to cheat."
Fahey's comments, however, came on the same day as global athletes' group UNI Sport Pro slammed WADA.
"The Lance Armstrong doping scandal and the Australian Crime Commission investigations demonstrate the ineffectiveness of the current WADA testing regime," it said.
