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.
A report from the Commission on Combating Drug Addiction and the Opioid Crisis said almost two thirds of overdoses are linked to opioid drugs such as heroin, fentanyl, and Purdue Pharma's Oxycontin (oxycodone).
Some 2.4 million Americans are estimated to be addicted to the drugs.
It came as he unveiled an anti-opioid abuse plan, which included his death penalty recommendation, new funding for other initiatives and stiffer sentencing laws for drug dealers. "And that toughness includes the death penalty", he said.
Trump has expressed his preference of the "ultimate penalty" for some drug traffickers in recent speeches, but this would be the first time the idea becomes part of an official plan.
On Monday, Health and Human Services Secretary Alex Azar said the new proposals will focus on "how we decrease the price of drugs and how we bring discounts that the middlemen right now are getting, how those will go to our patients".
Around 55 per cent of Americans are in favour of the death penalty for murder, the lowest levels in decades.
This is Trump's first visit as president to New Hampshire.
Drug-related murder is already a capital offense in the United States, but no one has ever been executed using those rules.
Pharmaceutical companies will ultimately have a role in remedying the opioid crisis, under Trump's plan.
"At the Department of Justice, we have made ending the drug epidemic a priority", Sessions said in a statement. The Department of Justice is working very, very hard on that. On top of that, Congress should consider legislation making it explicitly clear that no future President can require members of his staff, Cabinet officials, or anyone else to sign confidentiality agreements beyond those agreements necessary to ensure the secrecy of classified information.
The US president seemed to accept on Monday that his policy faced an uphill battle. Specifics of which cases would warrant the death penalty have yet to be released. "Maybe our country's not ready for that".
What does the rest of the world do?
As the United States continues to struggle with an opioid addiction crisis, President Donald Trump plans to get the federal government involved to help find a solution.
"I think he's going to like to talk about some of the good things the city of Manchester is doing, including Safe Station", Goonan said.
The official did not offer greater detail on how the death penalty could be invoked against drug dealers without amending statutes.
But Iran also imposes the death penalty for drug use, yet it is plagued by opiate addiction.
Trump convened an opioid commission a year ago, which introduced its final recommendations on how to curb the epidemic November 1.
The plan also calls for prevention, with a goal of reducing the number of opioid prescriptions by one-third over the next three years.