"It's more popular to have the position of the governor than my position," Santos said.
Annan praised Perry for "beginning to roll that [criminalization of drugs] back in Texas."
"I think what you are doing is right... and I applaud you," the former U.N. leader said.
At one point during the panel discussion, Annan all but endorsed modifying the international treaties that compel parties to ban drug use and trafficking.
"We have enough [evidence] in key countries to be able to make a judgement about whether the policies we have today are working," he said. "It's moved up the political agenda now and I don't think we can push it back."
A poll released Monday by CBS News found 51 percent of Americans believe marijuana should be legal. Other polls confirm widespread support. An October poll conducted by Gallup found 58 percent favor legalization.
The high-profile discussion Thursday was eagerly embraced by pro-legalization activists, some of whom formerly fought on the front lines of the so-called "War on Drugs."
"Drug prohibition fosters violence, enriches criminal organizations, destabilizes the institutions of civil society, and only makes the public health challenge of addiction worse," says former Drug Enforcement Administration Senior Intelligence Research Specialist Sean Dunagan, a member of the group Law Enforcement Against Prohibition. "The World Economic Forum is the perfect venue for world leaders to discuss alternative policies that will take the multi-billion dollar drug trade out of the hands of criminals and into a well-regulated, legal framework."