The cuts were far less severe in the official budget proposal that Mr. Trump submitted last month — about 3 percent instead of 95 percent — but Mr. Trump has proposed other cuts, including to the Community Development Block Grant Program, that could put certain drug treatment and mental and public health programs at risk.

John P. Walters, who led the Office of National Drug Control Policy under President George W. Bush, said he hoped the Trump administration would approach the opioid problem with “a much more extensive surveillance effort,” saying a federal lag in reporting overdose data was “shameful.”

“I think we need a revolution here, and at its essence has to be to truly understand this as an epidemic and begin to map it, follow up, find individuals who are at risk and more aggressively encourage them to get treatment,” he said.

On the interdiction side, “you need to treat this like a live shooter incident,” Mr. Walters added. “If somebody is distributing something that you now know is causing people to collapse and be at the risk of death, you need to try to find them and stop them, not just have extra bandages to treat the wounded. We’re not there yet.”

Mr. Trump’s budget proposal calls for an additional $103 million for the Department of Justice to fight the flow of heroin and other illicit drugs into the country.

In April, the Trump administration sent nearly $500 million to the states for addiction treatment through a new law, the 21st Century Cures Act, which was enacted with bipartisan support last year and signed by Mr. Obama. It will provide an additional $500 million next year. Another law passed last year, the Comprehensive Addiction Recovery Act, is also helping expand treatment and prevention through grants.