Related: Implementing alternatives to opioids among employees: what to know

Opiant Pharmaceuticals Inc., which makes Narcan and licenses it to Adapt Pharma, surged as much as 56 percent after Trump invited an Adapt executive to join him on stage and discuss the charitable program.

Trump has vowed since his 2016 campaign to curb drug abuse, which caused more than 64,000 overdose deaths last year, according to the Centers for Disease Control. The president has attached the effort to his call for a wall along the southern U.S. border, saying it would cut the illegal flow of drugs and people who sell them.

"Eventually the Democrats will agree with us" to build the wall and "to keep the damn drugs out," Trump said.

The president's plan calls for the Justice Department to seek the death penalty against drug traffickers "where appropriate under current law." The president argues that drug dealers are responsible for more fatalities than murderers sentenced to death.

Potentially unconstitutional

Critics have warned that the president's effort might be ruled unconstitutional by the Supreme Court, which in 2008 limited the death penalty to crimes that result in a victim's death or crimes against the state, like treason, espionage or terrorism. Death penalty cases also cost the government substantially more to prosecute.

"The draconian law enforcement provisions included in this proposal are unconstitutional and absurd," Jesselyn McCurdy, the deputy director of the American Civil Liberties Union Washington legislative office, said in a statement.

Separately, the president called on Congress to pass laws lowering the drug-possession threshold to trigger mandatory minimum sentences. Trump, who last year declared the opioid crisis a national health emergency, said he would start a public awareness campaign to reduce Americans' dependence on the drugs. But he has stopped short of declaring a national state of emergency as suggested by the presidential commission he empaneled to study the issue.

Trump was quoted last year by the Washington Post as having called New Hampshire "a drug-infested den" in a call soon after his inauguration with Mexican President Enrique Pena Nieto.

The president also said the Justice Department is "looking very seriously at bringing major litigation" against some drug companies that produce opioids. He said he wants to address the problem of over-prescribing and boost research of non-addictive painkillers. The administration also plans on "spending a lot of money on great commercials" that show the ill effects of drug addiction.

"The best way to beat the drug crisis is to keep people from getting hooked in the first place," Trump said.

Trump was joined on the trip by embattled Attorney General Jeff Sessions, whom the president has repeatedly and publicly criticized for having recused himself from Special Counsel Robert Mueller's investigation into Russia's meddling in the 2016 election. Sessions has been subject to rumors that he could be among the next top-level administration officials to lose their jobs after the departure last week of Secretary of State Rex Tillerson.

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