WASHINGTON — A White House review of hostage policy is likely to recommend that the government not block ransom payments by family members seeking release of captives, a U.S. official said Sunday.

The family of Warren Weinstein, the American aid worker taken hostage in 2012 and killed accidentally in a U.S. drone strike in January, reportedly paid a ransom in violation of the policy, hoping it would lead to his release.

Weinstein and an Italian man were killed in a strike targeting a compound thought to be frequented by al-Qaida militants, President Obama announced last week in a rare public admission of a grave targeting error by a U.S. drone attack. Obama has embraced the drone strikes as his preferred method of conducting counterterrorism operations overseas, but the hostage deaths brought renewed scrutiny.

The White House said after confirming the deaths of the men that it is considering changing its approach to overseas hostage rescues.

The change to the ransom policy would loosen U.S. protocol, which forbids such payments to obtain hostages’ release. The official said the prohibition on ransom payments by the U.S. government would be unaffected by the proposal, which was first reported by ABC News.

The proposal to permit family-paid ransoms “could make sense,” U.S. Rep. John Delaney, D-Md., whose congressional district includes Weinstein’s hometown of Rockville, Md., said on ABC’s “This Week.”

Richard A. Clarke, a former U.S. counterterrorism official, argued that lifting the blanket ban on ransom payments would encourage the taking of additional hostages.

“If you say that we’ll pay them, there’ll be many more hostages,” he said on “This Week.”