Ms Hulse stressed she was speaking personally and not for the council.
Mayor Len Brown said through a spokesman that he welcomed last week's ban on synthetic cannabis but also supported the status quo, which bans natural cannabis.
"He is comfortable with the fact that Penny has a view of it," the spokesman said.
Another councillor who heard Ms Hulse's comments, former senior police officer George Wood, said he strongly opposed her view.
"We would just be opening the floodgates if we legalised cannabis. We have got enough problems with alcohol and other drugs," he said.
"I was surprised when Penny said that this morning. I don't know if she has really thought it through."
Ms Hulse said she was speaking as "someone from a scientific background" with "a deep and abiding passion for science". She personally loathed cannabis.
"I have two grandchildren. The idea that they would choose to smoke cannabis or any legal highs breaks my heart," she said.
But toxicologists had shown that natural cannabis contained several compounds with an anti-psychotic effect to balance the psychoactive effects of tetrahydrocannabinol (THC), so it was less dangerous than synthetic products designed to match exactly receptors in the brain.
Despite last week's ban on 41 synthetic cannabis products, the Government still planned to allow the sale of synthetic products that could be shown in clinical trials to have a low risk. But last week's amended law also banned animal trials for recreational drugs, and that meant there was now no safe way to test their safety.
"Without animal testing it's a desktop exercise," Ms Hulse said, "and if you do a desktop exercise of a theoretical combination as a result of chemical experiments, well then you are basically saying let's go out and test them on our kids and our families.
"My concern is that we now go, 'We have banned them, we are going to do this sort of theoretical testing of them, then suddenly the way forward will emerge'.
"And I think we are kind of missing the point, which is that these so-called legal highs may never be safe and continuing to ban them out of hand is not an option without looking at alternatives."
Council staff said the national "legal high" market was estimated at $140 million a year before the ban and each shop was selling an average of $40,000 to $80,000 worth a week.