The United States has put forward a new proposal that would secure the release of a handful of living hostages held by Hamas in exchange for a month-long extension of the Israel-Hamas ceasefire, a source familiar with the negotiations said.

The two sides are supposed to negotiate a second phase of the cease-fire agreement that would end the war, but they remain far apart on how to move forward.

Trump's special envoy said gaining the release of Edan Alexander, believed to be the last living American hostage held by Hamas, was a "top priority."

The move is part of an escalating pressure campaign, but the Palestinian enclave gets most of its power from generators.

While fighting has not resumed since the March 1 ceasefire expiration, Israel has cut off humanitarian aid to Gaza to press Hamas.

U.S. Envoy for Hostages Adam Boehler was dropped by the Trump administration on Thursday because he defended Hamas soldiers during a CNN interview.