The International Cycling Union's (UCI) Irish president Pat McQuaid has been criticised for scrapping the commission.
But he hit back last night, accusing WADA president John Fahey of having a "personal vendetta" against cycling.
McQuaid said: "We have now reached this sorry juncture because WADA publicly questioned the independence of the independent commission.
"I would therefore urge the president of WADA one more time to try to set his personal vendetta and crusade against cycling aside and to support the UCI in doing what is right for cycling.
"Our aims are the same: to rid cycling and indeed all sports of the scourge of doping."
The UCI's decision to terminate the independent commission - whose members include Baroness Tanni Grey-Thompson - followed weeks of wrangling with WADA over its powers and whether those who testified could receive an amnesty.
The central issue of the inquiry concerned two donations by disgraced drugs cheat Armstrong to the governing body, and whether there was any complicity by the UCI in covering up his doping.
The UCI announced on Monday it was scrapping the inquiry in favour of a 'truth and reconciliation' process. McQuaid claimed WADA had agreed to this - something denied by the agency.
Fahey said: "The UCI has again chosen to ignore its responsibility to the sport of cycling in completing such an inquiry and has determined to apparently deflect responsibility for the doping problem in its sport to others.
"UCI has publicly announced that WADA has agreed to work with it on some form of truth and reconciliation. This is not only wrong in content and process, but again deceitful.
"WADA has not and will not consider partaking in any venture with UCI while this unilateral and arrogant attitude continues."
A statement from the commission also pointed the finger at McQuaid.
It said: "Pat McQuaid stated that the UCI 'will co-operate fully with the commission'...and urged all other interested stakeholders to do the same.
"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."
The pressure group Change Cycling Now (CCN) has also weighed in and called for the UCI's leadership, including McQuaid, to be removed.
Grey-Thompson attempted to stay out of the row but called on the UCI to disclose all the evidence.
She said: "Confidence in the integrity of the UCI is vital for the sport of cycling. It is essential that they make full disclosure of all documentation and evidence to allow the sport to move on and regain its standing and reputation."