Labour's Lewis MacDonald has welcomed the proposal to reduce the limit but said it could potentially have resource implications at a time of cuts to police backroom staff.
"I am not, in principle, opposed to the further devolution of more powers in this area but I am concerned to see the legislation come forward using the powers that are devolved already in order for that to provide the basis to go forwards," he said.
Mr MacDonald praised the former Labour government at Westminster for commissioning Sir Peter North's independent review of the law on drink and drug driving.
"Random testing, for example, was one of the North recommendations that he was able to elucidate strong evidence for," he said.
"I think some of the other issues raised are less evidence-based but I don't think the priority at this stage is the debate around those powers.
"The priority is to ensure that the powers that we have are implemented effectively."
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Sir Vince Cable, Caroline Lucas, Tony Robinson and Gina Miller led a demonstration on the second anniversary of the EU referendum.
Turning hot over the next few days. High pollen and UV levels.
The march took place on the second anniversary of the EU referendum.