Olympic and World Champion Bettini told Gazzetta dello Sport on Monday that the UCI plan to ask every rider for DNA samples was like being compared with "serial killers".
And Valverde has chipped in to the debate, saying: "I will not participate. That is a violation of my privacy. Cycling has gone too far."
Meanwhile, the Spanish parliament has approved a bill that will establish tough measures to tackle doping.
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Judicial processes will be streamlined and a new body, the Spanish Anti-doping Agency, will be charged with the prevention, control and investigation of doping within the country.
It will have the power to organise surprise blood tests away from events, as well as planned ones, and it will be a criminal offence to refuse to take a test.
The bill is scheduled to become law in the next six months and rather than solely targeting athletes is also designed to hit the supply networks and individuals who administer drugs.
"This is a big step forward. The principle of zero tolerance is going to become a reality in this country," said sports minister Jaime Lissavetzky.
"Sportsmen support this law. They said it wasn't fair that only the competitors suffered. If it is possible to prove the people behind the sportsmen are encouraging and facilitating the use of drugs, they will go to jail.
"Doping itself will be a crime. This will make it easier to get convictions from a legal point of view."
Cyclists implicated in Operacion Puerto have been told they will not face punishment by the Spanish Cycling Federation but the investigation continues to pursue team officials and employees implicated in the scandal.
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