The early days of Israel’s crackdown generally proceeded quietly, as former Hamas ministers and lawmakers acceded to arrest and Palestinian families in the Hebron area watched soldiers conduct house-to-house searches almost like sport. But on Friday morning, Israeli troops “faced sporadic confrontations,” the military statement said, with rocks, gasoline bombs, grenades, fireworks and improvised explosives thrown at them, responding in some cases with live ammunition to what officials called a “life-endangering threat.”

Witnesses in Dura, a West Bank town of 28,000 near Hebron, said that Mohammed Jihad Dudeen, 15, was fatally shot around 5 a.m., as he and other youths hurled rocks at about 150 soldiers storming their neighborhood. “One of them crouched and opened fire on the boy,” said Bassam al-Awadeh, 42, who said he watched from about 150 yards away. “The boy was hit in his heart and his abdomen.”

By noon Friday, Mohammed’s mother, Aida Abdel Aziz Dudeen, 39, sat in her living room robed in black mourning clothes, clutching a portrait of her son as she wailed, “Why did you leave me? Why have you abandoned me? I want to see you again in my dreams.” The women beside her on the couch, also wearing black, tried to comfort Ms. Dudeen by saying that her son had gone to paradise as an Islamic martyr.

A neighbor, Iman Abdel Alal, said Israeli troops damaged her home as they searched it in the early hours. “The soldiers kept me and four children and my husband in one room and told me, ‘You are Hamas!’ ” Ms. Alal said. “This has made me very angry. I will not have any sympathy with the soldiers. They killed many of us, but because of the kidnapping of three boys, they turn the whole world against us.”

Mohammed was the second Palestinian casualty in Israel’s operation, afterMonday’s death of a 20-year-old in the Jalazoun refugee camp near Ramallah. Palestinian news organizations reported that there were also clashes Friday in the Qalandiya refugee camp outside Ramallah, seriously wounding three young men, and in Bethlehem’s Dheisheh camp, where five were hurt.

One of the three hurt in Qalandiya, Mustafa Alsan, 20, was fighting for his life in an Israeli hospital Friday afternoon after being shot in the head.

“It’s to be expected that there will be some more friction on the ground,” Lt. Col. Peter Lerner, an Israeli military spokesman, said.

“The mission is ongoing. It is a substantial mission, the most substantial mission in Judea and Samaria since 2002,” Colonel Lerner said, using the biblical names for the West Bank. “But it is the most substantial terrorist attack in Judea and Samaria also in recent years. People can’t expect to just hijack little boys on their way home from school and we won’t do anything about it.”

The three teenagers — Eyal Yifrach, 19, Gilad Shaar, 16, and Naftali Fraenkel, who is also 16 and is a citizen of both Israel and the United States — were last heard from on June 12 around 10 p.m. as they hitchhiked homefrom their yeshivas in West Bank settlements. One of the teenagers called a police hotline and whispered, “I’ve been kidnapped,” but the authorities thought it was a crank call and did not begin their search for hours.

Tension was mounting not only between Israeli troops and Palestinian residents, but also between the Palestinian factions whose April reconciliation pact paved the way for a consensus government that wassworn in June 2. President Mahmoud Abbas of the Palestinian Authority has condemned the kidnappers and pledged not to let the situation descend into an intifada, or uprising, prompting harsh criticism from his Hamas partners.

“We are capable of igniting a third intifada, and no one will be able to prevent this right of ours once the pressure on the Palestinian people mounts,” Salah al-Bardaweel, a prominent Hamas leader in Gaza, said on Thursday. “We will not stand idly by in the face of the crimes of the occupation in the West Bank.”

Another Hamas spokesman, Sami Abu Zuhri, condemned the coordination between Palestinian Authority security forces and Israeli troops, after Mr. Abbas promised Wednesday that those forces would help find the missing teenagers and hold their captors accountable.

“These statements do not represent the Palestinian people,” Mr. Abu Zuhri said at a news conference in Gaza on Thursday night. “We have passed the weakness to challenge, waiting to take the initiative, complaining of confrontation, and we have strength cards.”

With the reconciliation on the brink of collapse, the prime minister of the consensus government, Rami Hamdallah, on Friday visited Hebron, the center of the Israeli operation.

Riyad al-Malki, the Palestinian Authority foreign minister, acknowledged Friday that if Hamas were culpable for the kidnapping, it would threaten the new government, but demanded that Prime Minister Benjamin Netanyahu of Israel provide proof and called Israel’s reaction “exaggerated.”

“If Netanyahu has any evidence, he has to put it on the table,” Mr. al-Malki told Agence France-Presse at a conference in Paris. “Three kids have disappeared but in exchange for that the Israeli Army has taken 300 Palestinians,” he added. “Their reaction went beyond logic, and what infuriates me the most is the lack of reaction from the international community.”

Alongside the arrests, Israel has tightened restrictions on Palestinian travel around Hebron; limited exit from the West Bank into Jordan; all but closed its crossings into Gaza; and punished Palestinian prisoners in Israeli jails, particularly those connected to Hamas, by, for instance, cutting back family visits.

On Friday, men under 50 were barred from the Temple Mount in Jerusalem’s Old City, where Israeli soldiers were out in force. Gaza militants have also fired rockets into southern Israel daily for a week, prompting repeated Israeli airstrikes; early Friday, Israel bombed five Gaza sites.

Mr. Netanyahu met Friday with the families of the missing teenagers, while his wife, Sara, joined a social media campaign by posting a photo of herselfwith a #BringBackOurBoys sign, mirroring a campaign around the abduction of Nigerian schoolgirls.

Bat-Galim Shaar, Gilad’s mother, said afterward that the parents had asked Mr. Netanyahu to do more. “We believe the government has other means of pressure that could expedite the return of the boys,” she said, the Israeli news site Ynet reported.

Yoav Limor, writing in the free daily Israel Today, said the military “has nearly maximized its ability to attack Hamas’s infrastructure” and that its leaders “are worried about increasing friction with the Palestinian civilian population.”