Hamas said Monday it accepted an Egyptian-Qatari cease-fire proposal, but Israel said the deal did not meet its core demands and it was pushing ahead with an assault on the southern Gaza city of Rafah. Still, Israel said it would continue negotiations.

The high-stakes diplomatic moves and military brinkmanship left a glimmer of hope alive — but only barely — for an accord that could bring at least a pause in the 7-month-old war that has devastated the Gaza Strip. Hanging over the wrangling was the threat of an all-out Israeli assault on Rafah, a move the United States strongly opposes and that aid groups warn will be disastrous for some 1.4 million Palestinians taking refuge there.