Palestinians in Gaza have spent almost two years longing for an end to the war that has destroyed their communities and killed tens of thousands of their neighbors. Many say their best hope yet is the latest cease-fire plan proposed by the United States — if only Hamas would accept it.

“Hamas must say yes to this offer — we have been through hell already,” said Mahmoud Bolbol, 43, a construction worker who has remained in Gaza City with his six children in the battered shell of their home throughout the war.

President Trump unveiled the proposal while meeting with Prime Minister Benjamin Netanyahu of Israel at the White House on Monday. Mr. Trump said that if Hamas did not accept its terms, then he would give Israel the green light to “finish the job” of destroying the armed group.

Hamas has not yet given its response to the proposal, but interviews with Palestinians in Gaza on Wednesday suggested widespread public support for the plan. It calls for an immediate end to a war that has brought immense civilian suffering.

For the past two days, Mr. Bolbol said, his neighbors have talked about almost nothing but the cease-fire proposal. If Hamas rejects it, he said, his family would finally leave Gaza City and head for what he hoped would be the relative safety of the enclave’s south.

“Hamas needs to understand: Enough is enough,” Mr. Bolbol said. Most Gazans are not members of the group, he added, “so why drag us into this?”