Howard Lutnick, the U.S. secretary of commerce, said in an interview on Tuesday that the tariffs President Trump imposed on Canada, Mexico and China could be lifted if those countries proved to Mr. Trump that they were stopping the flow of fentanyl and reducing the number of fatal fentanyl overdoses in the United States.

“You’ve seen it: It has not been a statistically relevant reduction of deaths in America,” Mr. Lutnick said on CNBC. “It’s just black and white. And we told them it was outcome based.”

But fentanyl-related overdose deaths have already been steeply declining over the past year, according to preliminary data published by the Centers for Disease Control and Prevention that the Trump administration promoted just last week.

Between September 2023 and September 2024, roughly 87,000 people died of drug overdoses, a decline of almost 24 percent compared with the same period a year earlier, according to the most recent C.D.C. update. Around 55,000 of the deaths were attributed to synthetic opioids such as fentanyl, a decrease of around 30 percent.

Overdose data lags by several months, as states confirm deaths and report them to the C.D.C., which then publishes national figures. Mr. Trump has suggested without evidence in recent weeks that the numbers are a significant undercount.

“We lose 300,000 people a year to fentanyl,” Mr. Trump said at a cabinet meeting last week. “Not 100, not 95, not 60, like you read. You know, you’ve been reading it for years. We lost, in my opinion, over the last couple of years, on average, maybe close to 300,000 people dead, and the families are ruined.”

The decrease in fentanyl overdoses, drug policy experts have said, has more to do with public health measures than changes in border policies. During the Biden administration, naloxone, an overdose-reversing medication, was approved for over-the-counter sales and became more widely available. Federal grants allowed communities to stockpile the rescue drug.

Buprenorphine, a treatment for opioid addiction, has also been easier to find for some drug users, after some restrictions for prescribing it were lifted by Congress in 2022.

While fentanyl causes the majority of fatal overdoses, other street drugs play a major role, including stimulants like methamphetamine and cocaine, and xylazine, an animal tranquilizer that can sedate a drug user for hours and does not respond to overdose reversal medication.