He said he wouldn't push for legislation, but if there is a lawmaker interested in sponsoring a bill, he would be willing to testify in favor of it.
Under current Utah law, possession of less than an ounce of marijuana can lead to a sentence of six months in jail and a $1,000 fine. The sale of any amount can result in a five-year sentence and a $5,000 fine.
Rep. Rebecca Chavez-Houck, D-Salt Lake City, said medicinal marijuana is an issue she has been interested in for some time and would like to see the Legislature study, although she doesn't anticipate sponsoring legislation in the upcoming session.
"It's one of those things we need to strike a very delicate balance, pursuing medical marijuana policy here in Utah," she said. "I understand it's very challenging."
She said she has heard from individuals and their family members who say it is useful for chronic pain management, and she is intrigued by New Mexico's policy, which has tighter controls than other states.
"For folks suffering from these challenges, these chronic diseases, to have that as an option is something that we shouldn't immediately say no," she said. "It's a very black-and-white issue for a number of people, and it shouldn't be that way."
Other Utah legislators say they would oppose any bill legalizing the drug for any purpose.
"I am always open to discussion on things, but I'm already decided personally on that one," said Sen. Allen Christensen, R-North Ogden, chairman of a Senate health committee.
Christensen said he understands the argument that it can ease pain and nausea for patients, but added that, based on what he has read, other states that have legalized medicinal marijuana have been unable to keep it under control.
"Like a lot of things, they have a good purpose," he said, "but they get misused and abused."
Rep. Paul Ray, R-Clearfield, said he would like to see marijuana studied to see if there really are benefits to its use. But it would take a change to federal law to allow that, he said.
In 2009, the Obama administration issued a memo directing federal prosecutors not to take action against states that have adopted medical marijuana laws as long as there are adequate controls in place.
Shurtleff agreed that any Utah program would have to have strict controls.