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.

Israeli fire has killed eight people in the Gaza Strip over the past 24 hours even as a fragile ceasefire with Hamas has largely held.

An Israeli air strike killed four Palestinians in Gaza, the territory's civil emergency service said, as Arab mediators and the United States tried to hammer out differences between Hamas and Israel over a January 19 ceasefire agreement.