U.S. officials said efforts to reach a cease-fire between Israel and Hamas are nearing the final stages, as diplomats worked frenetically to bring the fighting to an end at last and also keep Iran from a retaliatory strike that might ignite a wider war.

“We are closer than we’ve ever been” to an agreement, U.S. President Joe Biden said in Washington Friday, hours after Egyptian and Qatari mediators and U.S. envoys concluded two days of talks in Doha and vowed to convene another round by the end of next week in Cairo. Biden deployed Secretary of State Antony Blinken to Israel, with the top U.S. diplomat set to depart Saturday to press for the deal.

A senior U.S. official outlined the fresh terms of the proposal, saying it would involve a phased approach, with Israel redeploying its troops as hostages are released while allowing unarmed Palestinian civilians to return to their homes. It closely resembles a plan Biden unveiled in May to halt the violence and free the hostages Hamas still holds in exchange for Palestinian prisoners.