Patrice Clerc, boss of the Amaury Sports Organization (ASO) that owns the 104-year-old race, said a new way must be found to restore cycling's credibility following a succession of doping scandals at the Tour.
"The piloting of cycling's reconstruction can not be given to the UCI," Clerc said. "We will have to do it with all those who reject the current system in order to find our values again: riders, teams, sponsors, federations ... will all need to unite."
McQuaid was not invited to the race by organizers, but showed for Saturday's 19th stage time trial with an invitation from a French television station.
Asked for his reaction by The Associated Press, McQuaid said he "would never do anything to hurt the Tour de France" and that it was "scandalous" for Clerc's ASO to suggest that.
The feud between the two has been building since October 2005, when Clerc accused the UCI of not doing enough to combat doping.
"We will take the initiative in this debate," Clerc said. "We will communicate the results of our work on October 25, when we will announce the 2008 Tour route."
The feud got worse at this year's Tour because of more doping cases, forcing the ASO to kick out Alexandre Vinokourov, his Astana team, and Italian rider Cristian Moreni, which caused the withdrawal of Cofidis.
Clerc blames the UCI for not implementing a stronger doping program, and for allowing Michael Rasmussen to start the race even though he lied before the Tour and missed doping tests.