A DNA database containing details on all people in the UK would create a "nation of suspects", the Tories say.
Mr Davis said a universal register could damage civil liberties
Shadow home secretary David Davis said allowing the state to hold profiles would be "incredibly intrusive" and called for an "effective" debate.
A senior police officer has suggested a universal register, after two killers were convicted using DNA evidence.
The Home Office has ruled this out, saying it would raise "significant practical and ethical issues".
Sally Anne Bowman's killer, Mark Dixie, and Suffolk serial murderer Steve Wright were both captured because their DNA was taken after unrelated offences.
Speaking on BBC One's Andrew Marr Show, Mr Davis said: "Do we want to turn Britain into a nation of suspects? We have always had a presumption in our law, our basis of freedom, that people are not guilty until found guilty."
He said a universal database risked "changing the relationship between the ordinary citizen and the state".
Mr Davis added: "The simple truth is that fingerprinting has been around a long time. There's never been a call for a fingerprinting database. The same argument applies that we are criminalising the whole population... DNA is an incredibly intrusive thing."
He said there had to be a debate about making the use of DNA information "more effective but with the minimum intrusion to the liberties of the British citizen".
Meanwhile, former home secretary David Blunkett suggested the database could be extended on a voluntary basis.
He told Sky News: "I don't think the government could possibly go snap and just say well let's move from those who have committed a crime or been arrested to the whole population.
"I don't think in one go that is a feasible proposition, but I think actually saying to people you've got nothing to fear from this so long as we legislate to protect you."
The Liberal Democrats have said the party is opposed to the idea of a national system, saying it did not "stack up on practical grounds".
The Association of Chief Police Officers is calling for a debate on whether to expand the current database - of DNA details taken from crime suspects - to cover all people in the UK.
Both killers were convicted with compelling DNA evidence
Wright was on the existing system after being convicted of theft in 2003, and when police found his DNA on the bodies of some of his victims they matched it with his profile.
But Dixie was not on the system at the time of Sally Anne Bowman's murder in 2005.
It was only when he was arrested for assault after a fight in a bar nine months later that his DNA was taken and he was linked to the murder. He was arrested within five hours.
Det Supt Stuart Cundy, who led the murder hunt, said: "It is my opinion that a national DNA register - with all its appropriate safeguards - could have identified Sally Anne's murderer within 24 hours."
The DNA database, which covers England and Wales, currently contains around 4.5m profiles - routinely taken from criminal suspects after most arrests.
It is already the largest of its kind in the world but is controversial.
Since 2004, the data of everyone arrested for a recordable offence - all but the most minor offences - has remained on the system regardless of their age, the seriousness of their alleged offence, and whether or not they were prosecuted.
The existing register could be threatened when the European Court of Human Rights is asked to rule next week on a test case of two Britons who want their details removed from the database.