Israeli Prime Minister Benjamin Netanyahu vowed on Monday to restore security "on all fronts" after surging violence that included rocket fire from Lebanon and Syria, and two more deaths.
Mr Netanyahu also reinstated Defence Minister Yoav Gallant, whose firing he announced last month.
Heavy clashes, shootings, rocket strikes and a car-ramming attack have marred a period when the Muslim holy month of Ramadan coincides with the Jewish Passover and Christian Easter.
The latest casualties were a Palestinian teenager and a British-Israeli mother, who succumbed on Monday to injuries from a West Bank gun attack that killed her two daughters.
The day after Israeli police on Wednesday stormed the prayer hall of Jerusalem's Al Aqsa Mosque — Islam's third-holiest site — more than 30 rockets were fired from Lebanon into Israel.
Israel said the attack was most likely launched by the Palestinian armed movement Hamas.
Israel then bombarded the Gaza Strip and southern Lebanon, aiming for "terror infrastructures" that it said belonged to Hamas.
"We will not allow the terrorist Hamas to establish itself in Lebanon", by acting on "all fronts", Mr Netanyahu told a news conference on Monday.
Palestinian-Israeli violence had already intensified since his new government took power in December, a coalition with extreme-right and ultra-Orthodox Jewish parties.
The latest surge came after he late last month announced a "pause" for dialogue on judicial reform legislation, which split the nation and caused divisions in his government.
Air strikes intensify as Israel retaliates on targets in Lebanon and Gaza - in pictures
Among the political casualties was Mr Gallant, who the Prime Minister dismissed on March 26.
Mr Gallant earlier called for a halt to the legislative process on judicial reforms because of national security concerns — threats by reserve military personnel not to report for duty.
Mr Netanyahu is battling very low levels of popularity. A recent survey showed him likely to lose if an election were held now.
He said on Monday that he and Mr Gallant had "difficult disputes" but he had decided to put them in the past.
"Gallant remains in his post and we will continue to work together for the safety of the citizens of Israel," Mr Netanyahu said.
Earlier on Monday government ministers joined a protest march by Jewish settlers, held under tight security in the north of the occupied West Bank.
In the latest shooting in the territory, Israeli forces killed a Palestinian youth, Mohammed Balhan, 15, and wounded two other people, the Palestinian Health Ministry said, during what the army described as a raid to arrest a "terror suspect".
Israel confirmed its troops were operating in the Aqabat Jaber camp, the site of previous deadly Israeli raids this year, near Jericho, where soldiers were seeking "to apprehend a terror suspect".
The army said troops responded with live fire after "suspects opened fire toward [soldiers], hurled explosive devices and Molotov cocktails".
They said a suspect was taken in by security forces.
Clashes erupted when the army entered the camp and surrounded several houses, according to Palestinian news agency Wafa.
A Palestinian security official told AFP that five people were arrested during the raid.
Hamas said it mourned the "young martyr" and praised those "standing up to this arrogant enemy".
The operation came as a Jerusalem hospital confirmed that a British-Israeli woman, Lucy Dee, died after being seriously injured in a shooting attack on Friday in the West Bank, which killed her two daughters, aged 16 and 20.
Their car came under fire in the Jordan Valley, near Jericho. The family were residents of Efrat, a Jewish settlement in the West Bank.
British Foreign Secretary James Cleverly tweeted that there could be "no justification" for the "senseless violence".
Israel has occupied the West Bank since the 1967 Arab-Israeli War and hundreds of thousands of Jewish settlers live in Israeli-approved settlements there, which are considered illegal under international law.
Hundreds of Israelis marched on Monday in the north of the West Bank, pushing for state approval of an Israeli settler outpost.
Several government ministers, including far-right National Security Minister Itamar Ben-Gvir, appeared at the march to Eviatar, whose residents agreed to leave in 2021 while officials examined their case.
Mr Ben-Gvir told the crowd that "the response to terror is to build" settlements.
Violence has flared since Israeli police stormed the prayer hall of Al Aqsa Mosque in a pre-dawn operation aimed at dislodging "law-breaking youths and masked agitators" they said had barricaded themselves inside.
Late Friday an Italian tourist was killed and seven wounded in a car-ramming attack in Tel Aviv.
The Israeli army also said it launched strikes on targets in Syria on Sunday after rockets fired from there landed in the Israeli-occupied Golan Heights.
The conflict has this year claimed the lives of at least 94 Palestinians, 19 Israelis, one Ukrainian and one Italian, according to an AFP count.
These figures include, on the Palestinian side, combatants and civilians, including minors, and on the Israeli side, mostly civilians, including minors, and three members of the Arab minority.
