Political figures said the tests would create a “serious incentive” to obey the rules and keep public spaces clean.
They said ministers should think about handing out “additional powers” to the city council and other local authorities to allow a roll-out.
Barking and Dagenham Council in London recently revealed it would become the first UK local authority to use DNA testing as an enforcement method.
Samples will be collected from animals by swab, officials said, and the dog’s profile added to a registry.
Genetic information will then be taken from dog mess and compared to the database, with tests reckoned to be 99.9 per cent accurate.
Registering dog DNA will also be compulsory in the London borough from next April, as wardens patrol 27 parks and open spaces.
Conservative MSP Murdo Fraser, convener of the Scottish Parliament’s economy, energy and tourism committee, said city leaders should follow Barking and Dagenham’s lead.
He said: “Creating this database will help encourage those who repeatedly allow their dogs to foul public areas to stop doing so and also help prevent responsible dog owners from being tarred as negligent.”
Last month, the Evening News revealed environmental wardens in the Capital were issuing only a tenth of the fines handed out in Glasgow, with just one fixed penalty notice issued for dog fouling every six months.
Opposition leaders said DNA testing for dogs should be “seriously looked at”.
Councillor Chas Booth, Green spokesman, said: “If it can be employed cost-effectively then it would be a very serious incentive for a dog owner to act responsibly and pick up after their pets. This initiative shows enormous potential to clean up our streets.”
City bosses said it was unlikely DNA testing would be rolled out in Edinburgh but stressed that they were examining a range of enforcement measures.
Councillor Lesley Hinds, environment leader, said: “We will be cracking down on dog owners in certain communities who refuse to clean up after their pets.”