Israel’s demand for lasting control over two strategic corridors in Gaza, which Hamas has long rejected, threatens to unravel cease-fire talks aimed at ending the 10-month-old war, freeing scores of hostages and preventing an even wider conflict.

Officials close to the negotiations have said Israel wants to maintain a military presence in a narrow buffer zone along the Gaza-Egypt border it calls the Philadelphi corridor and in an area it carved out that cuts off northern Gaza from the south, known as the Netzarim corridor.