DUBLIN — Brendan Kennedy wants his obituary to read: "I built companies that helped end the cannabis prohibition around the world."

He also predicts that recreational marijuana use will be "fully legal at the federal level in the United States within the next two years."

Kennedy, chief executive of a Silicon Valley-founded firm, Privateer Holdings, is competing to establish a national brand of pot. But his comments Wednesday on stage at Dublin's Web Summit come when there is little clarity that U.S. federal laws would allow such a potentially massive market and with little reliable data.

Next year's U.S. presidential election could further complicate a debate on the issue that has divided Congress, regulators and the American public.

"This is a civil rights, civil liberties issue," Kennedy said, without elaborating.

He said Canada, where pot use for medical purposes is already legal, would almost certainly be the first country to legalize recreational use of the drug at the national level. That likelihood was...