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.

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