Herbert has said he finds the firing squad "a little bit gruesome," but Utah is a capital punishment state and needs a backup execution method in case a shortage of the drugs persists.
"We regret anyone ever commits the heinous crime of aggravated murder to merit the death penalty, and we prefer to use our primary method of lethal injection when such a sentence is issued," Herbert spokesman Marty Carpenter said.
The measure's approval is the latest illustration of some states' frustration over bungled executions and difficulty obtaining the drugs. Utah is one of several states seeking new forms of capital punishment after a botched Oklahoma lethal injection last year.
States have struggled to keep up their drug inventories as European manufacturers opposed to capital punishment refuse to sell the components of lethal injections to US prisons. The Texas deadline is the most imminent, but other states are struggling, too.
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Though Utah's next execution is probably a few years away, Ray said he wants to settle on a backup method now so authorities are not racing to find a solution if the drug shortage drags on.
Opponents of the measure say firing squads are barbaric, with the American Civil Liberties Union of Utah saying the bill makes the state "look backward and backwoods."