WASHINGTON — President Obama will announce Wednesday that the government will no longer threaten criminal prosecution of the families of American hostages who are held abroad by groups like the Islamic State if they try to pay ransom for the release of their loved ones.

The change is part of a broad overhaul he is ordering to fix what the administration has acknowledged is a broken policy on United States captives, senior administration officials said.

In a presidential directive and an executive order enshrining the changes, Mr. Obama also plans to make it clear that while he is keeping a longstanding federal prohibition against making concessions to those who take hostages, the government can communicate and negotiate with captors holding Americans or help family members seeking to do so in order to ensure their safe return.

The policy directive will for the first time make official and public what has long been the United States government’s unspoken practice in some hostage cases, but one that has been inconsistently applied and poorly understood both inside federal agencies and among family members desperate to win the release of their relatives.