MEXICO CITY — America’s drug problem is shifting from illicit substances like cocaine to abuse of prescription painkillers, a change that is forcing policy makers to re-examine the long and expensive strategy of trying to stop illegal drugs from entering the United States.

This rethinking extends beyond the United States, where policy makers are debating how to better reduce demand for painkillers. The effects would also be felt here and in Central America: With the drug wars in Mexico inflaming violence, some argue that the money now used for interdiction could be better spent building up the institutions — especially courts and prosecutors’ offices — that would lead to long-term stability in Mexico and elsewhere.

“The policies the United States has had for the last 41 years have become irrelevant,” said Morris Panner, a former counternarcotics prosecutor in New York and at the American Embassy in Colombia, who is now an adviser at Harvard’s Kennedy School of Government. “The United States was worried about shipments of cocaine and heroin for years, but whether those policies worked or not doesn’t matter because they are now worried about Americans using prescription drugs.”

The same sense that there is a need for a new approach was expressed last week by Gov. Chris Christie of New Jersey, a former federal prosecutor, who declared the war on drugs “a failure” that imprisons people who really need treatment.