John Wadham, the Director of the civil rights group, Liberty, said police should not be allowed to keep the DNA of innocent people.
The Home Office said it would save time and money if the samples were preserved.
If the plans were adopted they would allow a dramatic increase in the use of DNA and fingerprint evidence.
Backfire
Mr Wadham said that the proposal to allow the police to keep the details of DNA profiling of volunteers was "deeply flawed", and warned that it could backfire by leading to fewer people co-operating with the police.
Alternatively, he said, the public might feel intimidated into agreeing to allow profiles to be stored, fearing that a refusal would place them under suspicion.
A Home Office consulation paper says the DNA profiles should be held on a database if those involved agree.
The government says this will save time, money and inconvenience.
The BBC's home affairs correspondent Jane Peel says DNA profiling is increasingly being used to catch criminals.
'Caught by dandruff'
Advances in technology have enabled police forensic scientists to make a DNA match on evidence as small as a single hair or a piece of dandruff.
In the past only blood would suffice.
DNA tests have been particularly successful in cases where police have had to test hundreds or even thousands of people.
But under current legislation, the tests have to be destroyed if someone is caught and convicted.
There have been 120 mass screenings in England and Wales, gathering an average of 4,000 samples at a cost of £40 each.
The increasing use of mass screenings meant some people were being approached more than once.
Not only is this a waste of money, but it has sparked fears that people will refuse to give samples on the grounds of duplication.
Mr Straw said the samples would only be stored with the donor's consent, and would be kept on a separate database to the National DNA Database. This contains samples from 600,000 offenders.
At the moment, around 600 matches a week are made on the database, which is the biggest in the world.
Intrusive
Mr Wadham also rejected plans to allow police officers to take fingerprints on the streets. He said more innocent people would be subject to unnecessary and intrusive harassment, in practice leading to a disproportionate effect on black people.
Officers would also be given the go-ahead to use electronic scanners to gather fingerprints from suspects rather than relying on ink pads and paper.
Northern Ireland
Scotland
Wales
England
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