In accordance with World Anti Doping Agency (WADA) rules, Riis, the current manager of the CSC team, would not normally be forced to hand back his prize of the fabled yellow jersey because the offence happened over eight years ago.
However the International Cycling Union (UCI) said Riis should give back his coveted prize in a symbolic gesture which could reinforce the sport's fight against drug cheats.
"Despite the rules laid down by the World Anti Doping Agency, the UCI calls on Bjarne Riis to hand back his yellow jersey, which is a symbol of his victory," the UCI said in a statement released in Oropa at the current Tour of Italy.
The sport of cycling has spiralled into disgrace in recent weeks as several of Riis's former Telekom teammates confessed to using banned substances, including one of the top cyclists of the past 15 years, Erik Zabel of Germany, as well as Rolf Aldag, Bert Dietz, Christian Henn and Udo Boelts.
Law of silence
Cycling, and the strict, unwritten rules which govern the behaviour of the peloton, has often been controlled by a law of silence which is very rarely broken.
However the UCI feels events this week provide the perfect opportunity for those who have sinned in the past to repent, and help put the sport back on a more positive footing.
"The admissions from Germany and Denmark show that today people are prepared to stand up and speak out, which is extremely positive, and the UCI calls on all other riders and their entourage who have been involved in doping to speak out," the statement added.
"Even though events in the past and present may go against us, there is now real determination from those involved in cycling to make major changes."
Operation Puerto
In May 2006 the 'Operation Puerto' affair uncovered an alleged doping and blood doping network based in Madrid, where it was run by Eufemiano Fuentes, a Spanish doctor.
After months of denials, Italian cycling star Ivan Basso, a former leader with Riis's CSC team until his sacking last autumn, recently admitted he was implicated in the affair with prosecutors for the Italian Olympic Committee asking for a 21-month ban on the rider.
Christian Prudhomme, Tour de France chief, meanwhile said Riis's admission should lead to the Dane quitting cycling altogether.
Black mark
"Bjarne Riis said it himself. He does not deserve to have won the Tour de France, because he cheated. He has left a black mark on the Tour de France," Prudhomme told AFP.
"Is this someone who should be leading a cycling team? He was the manager of Ivan Basso last year when Basso was in contact with Fuentes. Is there a link?
"I would like to have the answers to these questions," added the Frenchman, who, like the UCI, has called on others to repent to help save the sport.
"People have to speak out. We have to pull together to save this wonderful sport."
Support for Riis
Spaniard Carlos Sastre, CSC's main hope for the yellow jersey this July, defended his team manager.
"I have total faith in Bjarne, and he has all my support," said Sastre.
"He has made mistakes in the past, but since then he has fought hard to show the younger riders coming through the values of determination, training and sacrifice.
"It's a difficult time for Bjarne right now, but I want to say that despite what other people might believe, this team owes a lot to him."