Mr Trump was cheered on Monday as he told a crowd in Manchester, New Hampshire: "If we don't get tough on the drug dealers we're wasting our time".
Trump unveiled his plan to combat the nation's deadly opioid addiction in a speech Monday in Manchester, New Hampshire, a state ravaged by the drug.
"Failure is not an option, addiction is not our future", Trump said.
"If they provide the right support for those folks, which means help providing housing, help dealing with child care, then we'll see something happen", Kazel said.
Federal law now allows for the death penalty in drug cases that involve murder, such as those committed during a drive-by shooting or while trafficking drugs, according to the Death Penalty Information Center.
Azar, a former president of the USA arm of drugmaker Eli Lilly and Co, joined Trump at the New Hampshire event. He captured his first Republican presidential primary here in 2016, though he narrowly lost in the general election to Democrat Hillary Clinton.
The death-penalty element of Trump's drug plan has been criticized by public health experts and others who point out that numerous people addicted to opioids were hooked initially by legally prescribed drugs.
The plan calls for the U.S. Justice Department to seek the death penalty for large-scale drug traffickers under current federal law, which allows for capital punishment in drug-related cases that involve murder with the use of a firearm or the killing of a law enforcement officer.
Mrs. Trump spoke about her visits to hospitals and clinics that help children who were born addicted to opioids.
The President's speech got mixed reviews from those on the front lines of the state's opioid crisis.
The president has at times expressed admiration for countries with draconian penalties for trafficking drugs.
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Other parts of the plan include broadening education and awareness, and expanding access to proven treatment and recovery efforts.
Kevin Ring, president of Families against Mandatory Minimums, which campaigns against sentencing they see as too harsh, said Trump's plan calling for stiffer sentences or seeking the death penalty against drug dealers, was merely "doubling down on a failed strategy". The most recent event, Trump said, saw the agency collect 900,000 pounds of pharmaceutical products, "more than the weight of three Boeing 757s". "We'll do whatever we have to do", he said.
According to the Centers for Disease Control and Prevention, 42,000 people died from opioid overdoses in 2016, the latest year with publicly available data.
Meanwhile, Capitol Hill lawmakers from both parties are trying to put muscle behind Mr. Trump's decision last fall to declare opioid addiction a public health emergency.
The White House did not offer examples of when it would be appropriate to seek the death penalty for drug dealers and referred further questions to the Justice Department.
Trump's preference for executing drug offenders was first reported last month.
"Every day, sanctuary cities release risky individuals, drug dealers, traffickers, gang members back into our communities".
The president's focus on punitive measures alarmed some in the public health community. "These were great kids who had jobs and would have benefited their communities." she said.
The Granite State is an early primary state that already has been visited by potential 2020 GOP primary foes John Kasich (Ohio's governor) and Jeff Flake (a retiring Arizona senator).
Olson said Trump's proposal to reduce the number of prescriptions written for opioids might not address the underlying problems. He told Republicans someone needs to stop Trump - and it could be him if no one steps up.