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.


While a major change in policy is not imminent — “It’s all aircraft carriers, none of it moves on a dime,” as one senior Obama administration official put it — the election of a new president in Mexico, Enrique Peña Nieto, is very likely to have an immediate impact on the debate. Mr. Peña Nieto has promised to focus not on drugs but rather on reducing the violent crimes that most affect Mexicans.


Mexico and other countries nearby, especially Honduras, El Salvador and Guatemala, are withering under a metastasizing threat: violence caused by drug traffickers battling for power, to move drugs, extort businesses, and kidnap and kill for ransom. The American response so far has mostly involved a familiar escalation of force, characterized by the addition of law enforcement and military equipment and personnel to help governments too weak to combat trafficking on their own.


But in Mexico, a focus of American antidrug efforts in recent years, a shift in priorities is already apparent. Since 2010, programs for building the rule of law and stronger communities have become the largest items in the State Department’s antidrug budget, with the bulk of the money assigned to Mexico. That amounts to a reversal from 2008 and 2009, when 70 percent was allocated to border security and heavy equipment like helicopters.


Even some officials with the Drug Enforcement Administration and Justice Department say they now recognize that arresting kingpins and seizing large drug shipments have failed to make Mexico more stable, largely because of corruption and other flaws in the Mexican justice system.


American officials say they are now focused on training Mexican prison guards, prosecutors and judges, while supporting Mexican programs aimed at keeping at-risk youths from joining gangs.


“We see crime as the leading threat in some countries to economic growth and the leading threat to democracy,” said Mark Feierstein, the United States Agency for International Development assistant administrator for Latin American and the Caribbean.


Still, law enforcement remains a major element of the government’s strategy, as the deployment of a commando-style squad of D.E.A. agents in Honduras has demonstrated. And the Obama administration has ruled out drug legalization, despite expanding support for the idea in Latin America, while designating about 60 percent of the federal antidrug budget of roughly $25 billion a year to supply-side efforts, with 40 percent to demand, as the government has for decades.


Eric L. Olson, a security analyst with the Woodrow Wilson International Center for Scholars, said the growing debate had, so far, mostly led to confusion. “Some U.S. officials favor building institutions; others think it’s hopeless,” he said.


Other experts are more critical of the Obama administration, pointing to the continued focus on cocaine interdiction, especially in Honduras, where the D.E.A. squad has been involved in a series of recent raids. One left four people dead, including two pregnant women, and in another one, last week, two people who were said to be smugglers were killed.