The Nuffield Council on Bioethics also urged ministers to drop plans to take DNA from people who have committed less serious crimes such as speeding or littering.
The council said while the National DNA Database is a valuable crime-fighting tool, more safeguards are needed to protect the liberty and privacy of innocent people.
Currently, police can permanently store DNA taken from people who have been arrested even if they are later found to be innocent.
The council recommended that only DNA from convicted criminals should be archived.
The only exception should be samples from people accused of serious violent or sexual offences, which should be stored for five years, the experts said.
Council chairman Professor Sir Bob Hepple QC, emeritus master of Clare College and emeritus professor of law at Cambridge University, said: "Innocent people are concerned about how their DNA might be used in future if it is kept on the National DNA Database without their consent."
Police can take DNA samples - by force, if necessary - from anyone arrested for a "recordable" offence - in other words, mostly those offences that can lead to a prison sentence.
The DNA is then stored indefinitely on the National DNA Database, which currently holds more than three million samples.
In March the Government asked for feedback on whether laws should be changed to further expand these powers.
A review of the Police and Criminal Evidence Act suggested allowing officers to store DNA from people arrested for "non-recordable" offences, including dropping litter, fouling the pavement, throwing fireworks and trespassing on the railway, as well as some minor motoring offences such as speeding, failure to wear a seatbelt and parking offences.
Today's report said these proposals should be dropped.
Prof Hepple said: "After careful consideration, we do not think that this is justified at the current time.
"We would like to see the police put more resources into the collection of DNA from crime scenes, rather than from individuals suspected of minor offences."
Currently, fewer than 20% of crime scenes are forensically examined, said the report.
It also advised against setting up a universal DNA database of everyone in the country.
"This would be hugely expensive and would have only a small impact on public safety," said the report.
"The intrusion of privacy incurred would therefore be disproportionate to any possible benefits to society.
"For these reasons, the Nuffield Council is against the establishment of a population-wide forensic DNA database at the current time."
The council also urged ministers to change the rules on how DNA from children should be stored.
There are about 750,000 under-18s on the National DNA Database, and the experts said there should be a "presumption in favour" of removing their DNA from the database unless there was a good reason not to, such as having committed a very serious offence.
Victims or witnesses who volunteered to have their DNA added permanently to the National DNA Database should also be able to have their own samples removed at any time without having to give a reason, it added.
The experts also proposed new restrictions on "familial searches" for people with shared DNA profiles, and on police systems for allocating DNA samples to one of seven broad ethnic groups.
An independent tribunal should be set up to hear requests by individuals who want to have their DNA erased from the archive, and the way forensic databases are operated should be enshrined in law, it recommended.
Lawyers and judges should have a "minimum understanding of statistics" when they deal with complex DNA evidence, while jurors should be told about the "capabilities and limitations" of DNA evidence, today's report added.
The Forensic Science Service, which runs the database for the Home Office, can handle more than 10,000 DNA crime stain samples each month and about 50,000 DNA samples from individuals.
In addition, the 160 page report recommended slimming down the number of crimes for which suspects could have their DNA profiles taken by police.
The list of recordable offences should be "rationalised" to exclude all minor, non-imprisonable crimes, it said.
The report recommended spending more money on gathering and analysing samples from crime scenes, rather than expanding a number of profiles being obtained from suspects.
Today's study also covered the use of fingerprinting by police and recommended that fingerprint experts should make it clear when giving evidence in court that their conclusions were "always one of expert judgment and never a matter of absolute scientific certainty".
There was criticism of a "significant lack of transparency" concerning research which is carried out using the National DNA Database, the experts said.
It was also difficult to assess the impact of increasing police powers because of the "poor quality or absence of official statistics, or conflicting statistics."
The council's report concluded: "We recommend a far greater commitment to openness and transparency and a greater availability of documents to public scrutiny."
A Home Office spokeswoman said: "There are no Government plans to introduce a universal compulsory, or voluntary, national DNA database.
"The Government appreciates that some people may be concerned about building a larger DNA database, particularly where it relates to people who have not been proceeded against for an offence.
"However, we have concluded that given the clear evidence showing the substantial public benefit in relation to the detection of serious crime, the existing policy is justified.
"Inclusion does not signify a criminal record and there is no personal cost or material disadvantage to the individual simply by being on it."
She added: "It is estimated that there are about 200,000 profiles on the database which would have been removed prior to a change in legislation in 2001.
"From these, about 8,500 individuals have been matched with DNA taken from crime scenes, involving some 14,000 offences that include 114 murders, 55 attempted murders, 116 rapes, 68 other sexual offences, and a number of other serious crimes."
Liberal Democrat home affairs spokesman Nick Clegg said: "The retention of the DNA of thousands of innocent British citizens is an outrage and must stop.
"It blurs the fundamental distinction between innocence and guilt upon which our whole criminal justice system depends.
"It was the Liberal Democrats in government in Scotland who insisted on a system of DNA retention north of the border that protects the rights of innocent people.
"As the Nuffield study rightly points out, there's no earthly reason why that system cannot be adopted south of the border as well."
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