Israel's demand for permanent control over two strategically vital corridors in Gaza, a demand consistently rejected by Hamas, poses a significant obstacle to cease-fire negotiations aimed at ending the protracted 10-month conflict , securing the release of numerous hostages, and averting an even larger-scale conflict.

Sources close to the negotiations have disclosed that Israel seeks to maintain a military presence within a narrow buffer zone along the Gaza-Egypt border, designated as the Philadelphi corridor, and in a zone they have established that isolates northern Gaza from the south, known as the Netzarim corridor.

It remains uncertain if Israeli control of these areas is included in a U.S.-backed proposal that Secretary of State Antony Blinken has urged Hamas to accept to end the current stalemate in cease-fire talks. Blinken, who is back in the region this week, stated on Monday that Israel had agreed to the proposal but refrained from detailing its contents.

Israeli Prime Minister Benjamin Netanyahu asserts that control of the Egyptian border area is essential to prevent Hamas from replenishing its weapons through smuggling tunnels and that Israel needs a "mechanism" to stop militants from returning to the north, which has been largely isolated since October.

Hamas has rejected these demands, which were only publicly revealed in recent weeks. Earlier drafts of a developing cease-fire proposal seen by The Associated Press made no mention of Israel retaining control of the corridors.

Hamas contends that any lasting Israeli presence in Gaza would constitute military occupation. Egypt, which has played a pivotal role as mediator in the monthslong talks, also firmly opposes an Israeli presence on the other side of its border with Gaza.

The Philadelphi corridor is a narrow strip — about 100 meters (yards) wide in places — extending the 14-kilometer (8.6-mile) length of the Gaza side of the border with Egypt. It includes the Rafah Crossing, which until May was Gaza's only passage to the outside world not under Israeli control.

Israel claims Hamas utilized an extensive network of tunnels beneath the border to import weapons, allowing them to amass the military force used in the Oct. 7 assault that initiated the war . The military asserts they have identified and destroyed numerous tunnels since gaining control of the corridor in May.

Egypt denies these accusations, stating that it demolished numerous tunnels on its border long ago and has implemented its own military buffer zone to prevent contraband.

The Netzarim Corridor, stretching approximately 4 miles (6 kilometers) from the Israeli border to the coast south of Gaza City, divides the territory's largest urban center and the northern region from the south.

Hamas has demanded that the hundreds of thousands of Palestinians displaced from the north be permitted to return to their homes. Israel has agreed to their return but insists on ensuring they are not armed.

Israeli control over either corridor would necessitate closed roads, fences, guard towers, and other military installations. Checkpoints are among the most visible signs of Israel's ongoing military control over the West Bank, and over Gaza before its withdrawal in 2005.

Israel asserts that such checkpoints are essential for security, but Palestinians perceive them as a humiliating restriction on their daily lives. Many Palestinians would also view them as a precursor to a lasting military occupation and the re-establishment of Jewish settlements — a scenario openly advocated for by Netanyahu's far-right coalition partners.

Hamas has called for a complete Israeli withdrawal and accuses Netanyahu of imposing new conditions to undermine the negotiations.

Egypt contends that Israel’s actions along the border pose a threat to the historic 1979 peace agreement between the two nations. It has refused to open its side of the Rafah crossing until Israel restores the Gaza side to Palestinian control.

Israel maintains that these are not new demands, but rather clarifications to a previous proposal supported by President Joe Biden in a May 31 address and by the U.N. Security Council in a rare cease-fire resolution. Israel also claims that Hamas has introduced new conditions since then that it cannot agree to.

However, neither the address nor the Security Council resolution mentioned anything about Israel's demands regarding the corridors — which only became public in recent weeks — and both called for a full withdrawal of Israeli forces. The U.S. has also stated its opposition to any reoccupation of Gaza or reduction of its territory.

Previous written versions of the cease-fire proposal outline an initial withdrawal by Israeli forces from populated and central areas during the first phase of the agreement. This is when the most vulnerable hostages would be freed and displaced Palestinians would be allowed to return to the north.

During the second phase, the specifics of which would be negotiated during the first phase, Israeli forces would fully withdraw. Hamas would then release all remaining living hostages, including male soldiers.

The most recent drafts of the proposal — including one that Hamas agreed to in principle on July 2 — include language stipulating that displaced residents returning in the first phase must not carry weapons. However, they do not specify a mechanism for searching them.

The United States, Qatar, and Egypt, which have been actively involved in mediating an agreement for months, have not publicly commented on Israel's demands regarding the corridors.

An Israeli delegation engaged in discussions with Egyptian officials in Cairo on Sunday, focusing on the Philadelphi corridor, but did not achieve a breakthrough, according to an Egyptian official who spoke on the condition of anonymity to discuss the private meeting.

The failure to reach a cease-fire agreement would prolong a war in which Israel's offensive has already resulted in the deaths of over 40,000 Palestinians, according to Gaza health officials, displaced the vast majority of Gaza's 2.3 million residents, and caused extensive destruction within the impoverished territory.

Palestinian militants continue to hold approximately 110 hostages seized during the Oct. 7 attack that ignited the war, an attack that resulted in the deaths of roughly 1,200 people, primarily civilians. Israel has successfully recovered only seven hostages through military operations. According to Israeli authorities, about one-third of the 110 hostages have perished, and the remaining captives are in jeopardy as the conflict persists.

A ceasefire agreement also provides the best opportunity to prevent — or at least postpone — a potential Iranian or Hezbollah attack on Israel following last month's targeted assassinations of a Hezbollah commander in Beirut and a Hamas leader in Tehran.

Israel has pledged a retaliatory response to any attack, and the United States has dispatched military assets to the area, raising the possibility of a larger and more destructive conflict.

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Associated Press reporters Abby Sewell in Beirut and Samy Magdy in Cairo contributed to this report.

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Follow AP’s coverage of the war at https://apnews.com/hub/israel-hamas-war