The West Bank is home to about 2.7 million Palestinians and more than 500,000 settlers. Israel seized control of the territory from Jordan in 1967 during a war with three Arab states, and Israelis have since settled there with both tacit and explicit government approval, though the international community largely considers settlements illegal, and many outposts also violate Israeli law. Settlers are governed by Israeli civil law while their Palestinian neighbors are subject to Israeli military law.

Palestinians have long argued that the settlements are a creeping annexation that turns land needed for any future independent Palestinian state into an unmanageable patchwork. But the war with Hamas in Gaza has given Israel’s right-wing government, intent on West Bank expansion, a way to bolster settlers who oppose the creation of a Palestinian state under the guise of providing added security amid heightened tensions, some rights groups say.

The army has shut down “so many roads” in the West Bank that thousands of acres of land have become off limits to Palestinians, Hagit Ofran of Peace Now’s “Settlement Watch” project said in a phone interview. The military erects gates in the name of security, but the result is that it shuts off Palestinians’ access to large areas they rely on, she added, and that ultimately advances settlers’ aims.

Notably, there are also more Israeli troops stationed in the area than before the war. “In every settlement, you now have reserve soldiers who are settlers and who take extremist measures against Palestinians,” Ms. Ofran said. “Settler soldiers are actually an armed militia.”

Israel’s finance minister, Bezalel Smotrich, is a settler himself and responsible for extremist policies meant to expand Israel’s hold over the West Bank. Mr. Smotrich is taking away much of the military’s authority there and instead putting settlers in charge of civil administration, effectively taking control, Ms. Ofran noted. In a secretly recorded speech on June 9, Mr. Smotrich outlined this carefully orchestrated program to take authority over the West Bank out of the hands of the Israeli military and turn it over to civilians working for him while deflecting international scrutiny.

From the perspective of some in the Israeli military, settler violence is a threat to Israel’s security. Retired Maj. Gen. Yehuda Fox, former chief of Israel’s Central Command, which oversees the West Bank, rebuked the Israeli government’s policies in the area and condemned the rising tide of “nationalist crime” in his departure speech last week.

But as the military’s presence in the West Bank has increased since Oct. 7, so have violent clashes between Palestinians and Israeli troops meant to maintain order there, further escalating tensions in the already fraught region.

Israeli forces shot a man dead in the West Bank on Tuesday during clashes in Al Bireh, according to Wafa, the Palestinian Authority’s official news agency. The Israeli military did not immediately respond to a request for comment.

Israel’s military said on social media on Tuesday that it was chasing people who fired on a car with Israeli civilians inside in Ramin, a village in the northeast of the West Bank, adding that the civilians had been lightly injured in the attack and had been evacuated for treatment. It gave no further details.

Israeli forces have killed more than 530 West Bank Palestinians since the war in Gaza began, according to the United Nations Office for the Coordination of Humanitarian Affairs, which tracks West Bank violence on a weekly basis. In its latest update, the agency said that the Israeli military on July 9 killed a 13-year old Palestinian boy in Deir Abu Mash’al village near Ramallah and injured three other boys.

The Israeli military, in response to a query about the incident, said in a statement that since Oct. 7, there had been “a significant increase” in attempted terrorist attacks in the West Bank and nearby area — more than 2,000 in total — and that it is “actively conducting operations” to prevent terrorism. The military confirmed the U.N. report of violence on July 9, but not a death or the involvement of any children in the confrontation, stating that “masked terrorists hurled rocks” at Israeli military vehicles and a “soldier in the area responded with live fire, hitting one of the terrorists.”

Matthew Mpoke Bigg and Rawan Sheikh Ahmad contributed reporting.

Israel is reluctant to withdraw because it says that would make it easier for Hamas to restock its arsenal and reestablish authority over Gaza. Prime Minister Benjamin Netanyahu said in a statement on Friday that he “insists that Israel remain on the Philadelphi Corridor,” as some call the border area.

But in private discussions last week with the Egyptian government, senior Israeli envoys indicated that Israel might be willing to withdraw if Egypt agreed to measures that would prevent arms smuggling along the border, according to the three officials.

Measures that were proposed included installing electronic sensors along the border that could detect future efforts to dig tunnels, as well as constructing underground barriers to block tunnel construction, the officials said. All three requested anonymity in order to speak more freely about an idea that Israel has not publicly endorsed.

In public, both Israel and Egypt have been reluctant to confirm the existence of the talks. Mr. Netanyahu’s ruling coalition needs the support of lawmakers opposed to any truce that would leave Hamas in power, and his government could collapse if he acknowledges what his envoys are discussing in private.

The talks were first reported by Israeli news media and Reuters last week; Mr. Netanyahu swiftly dismissed the reports as “absolute fake news.”

But Mr. Netanyahu’s defense minister, Yoav Gallant, had suggested in a separate statement earlier in the week that Israel could withdraw under certain circumstances. “A solution is required that will stop smuggling attempts and will cut off potential supply for Hamas, and will enable the withdrawal of I.D.F. troops from the corridor, as part of a framework for the release of hostages,” the statement said, referring to the Israel Defense Forces.

When asked for comment on Monday, Mr. Netanyahu’s office referred The New York Times to the prime minister’s previous statement. The Egyptian government declined to comment.

A state-run Egyptian television channel, citing an unnamed Egyptian official, said on Friday that no agreement had been reached about the border — but stopped short of denying that Israeli and Egyptian officials had discussed the matter.

Aaron Boxerman and Emad Mekay contributed reporting.