Israel and Hamas are holding out for bigger gains in the Gaza war, helping explain the failure of the world's most influential diplomats to broker even a precursor to a lasting cease-fire. Here's a look at the leaders and nations involved and what each wants.
Hamas, which controls the Gaza Strip, wants to break the seven-year blockade of Gaza and believes the only way to force serious negotiations on ending the closure is to keep fighting.
Israel wants more time to destroy Hamas' rocket arsenal and military tunnels, and to inflict enough pain to deter the Islamic militant group from launching rocket attacks in the future. Israel views the tunnels, used by Hamas for launching attacks, as a major threat. Prime Minister Benjamin Netanyahu raised the idea of trying to disarm Hamas in the future, with international help, but hasn't said how.
Secretary of State John Kerry spent several days in the region last week to win agreement on an immediate weeklong truce, during which talks on a new Gaza border deal would begin. Israel's Cabinet rejected the idea, in part because it would have meant calling off tunnel demolitions.
The Palestinian president initially supported the position of Egypt, which called for both sides to stop fighting first and later discuss new border arrangements for Gaza. But Abbas has since adopted Hamas' cease-fire demands. Public opinion in the West Bank, where Abbas' power lies, appears to be turning against him. He is perceived as not doing enough to help Gaza's suffering civilians.
Egypt sealed border-smuggling tunnels between the country and Gaza in part because Hamas is a branch of the region's Muslim Brotherhood. Egypt's military deposed a Brotherhood-led government in Cairo last year. Egypt fears unrestricted movement between Gaza and Egypt through the Rafah border crossing will strengthen Hamas and fuel militancy in Egypt's restive Sinai Peninsula, next to Gaza.
Qatar is seen as a conduit for Hamas demands. The tiny Persian Gulf nation, which hosts several senior Hamas leaders, has condemned the Egypt-Israel blockade of Gaza and said the international community is "turning a blind eye" to Gaza's plight.
Turkey likely would see a role as a mediator in a broader deal on ending the Gaza blockade. It has close ties to Hamas and has been funding projects in Gaza, including the construction of a hospital. Prime Minister Recep Tayyip Erdogan has made no secret of his distrust of Egypt, recently accusing the Egyptian leader of blocking humanitarian aid from entering Gaza.