A former top adviser to President Barack Obama on Thursday expressed concern about “blowback” from the aggressive U.S. campaign of drone strikes, warning that the attacks could be undermining long-term efforts to battle extremism.

The former adviser, Gen. James E. Cartwright, is the latest and perhaps the most influential former member of Obama’s national security team to express concerns that the costs of the strikes might be beginning to outweigh the benefits. But Cartwright, a former vice chairman of the Joint Chiefs of Staff and a favored adviser during the president’s first term, also expressed skepticism about a draft administration proposal to gradually shift drone operations from the Central Intelligence Agency to the Pentagon.

Under the proposal, two U.S. officials said, the Defense Department would gradually assume control over drone operations outside Pakistan. The officials said that Obama, who has spoken publicly about his desire to make the program more transparent, had not yet made a decision about the proposal. Because it would probably leave drone operations in Pakistan under the CIA, the practical impact of such a move in the short term would appear to be limited.

Cartwright said that he worried about a “blurring of the line” between soldiers and spies if the Pentagon was put in charge of drone operations in sovereign countries “outside a declared area of hostility.”

If U.S. troops take over more nontraditional missions like targeted-killing operations beyond war zones, he said, the danger of “changing the ethos of the military” will grow.

Cartwright did not quarrel with government claims that the strikes had been precise in targeting militant suspects. However, he said that mistakes, however rare, could do serious damage to America’s reputation.

“We’re seeing that blowback,” he said. “If you’re trying to kill your way to a solution, no matter how precise you are, you’re going to upset people even if they’re not targeted.”

He spoke at the Chicago Council on Global Affairs.

In recent months, several former top military and intelligence officials — including Gen. Stanley A. McChrystal, the former senior commander in Afghanistan, and Michael V. Hayden, the former CIA director — have sounded similar warnings about the Obama administration’s reliance on drone strikes in Pakistan and Yemen.

Cartwright’s comments came amid a debate inside the Obama administration about bringing greater transparency to drone operations. But the impact of shifting drone operations to the Pentagon — a possibility first reported this week by the website The Daily Beast — would be blunted because a vast majority of the CIA’s strikes have been carried out in Pakistan. The CIA operates on its own there, having carried out 365 strikes, by the count of the Bureau of Investigative Journalism in London, compared with about 45 in Yemen and a handful in Somalia.

Many experts on national security believe that lethal operations like drone strikes should be carried out by the military, not the CIA. The military has deep experience in how to operate within the laws of war, has spent decades studying how to avoid civilian casualties and generally operates in a far more open fashion than the CIA.

But in recent years, the strikes have not always played out that way. In Yemen, Obama brought the CIA into the drone campaign in 2011 in part because several of the military’s strikes went awry, killing women and children and a popular deputy governor. Journalists have often been able to find out more about CIA strikes in Pakistan than strikes by the military’s Joint Special Operations Command in Yemen.