Israeli Prime Minister Benjamin Netanyahu vowed to restore security "on all fronts" after an Israeli attack on the Al-Aqsa Mosque last week led to spiralling violence that included rocket fire from Lebanon and Syria and two more deaths on Monday.
Netanyahu also reinstated the defence minister whose firing he announced last month.
Continuing raids of Palestinian towns by Israeli forces, stormings of the Al-Aqsa Mosque by Israeli extremists, 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 shot during an Israeli military raid in a refugee camp near Jericho. He was 15-year-old.
So far this year, at least 94 Palestinians have been killed by Israeli forces.
Also on Monday, a Jerusalem hospital confirmed that a British-Israeli woman, Lucy (Leah) Dee, had died after being seriously injured in a West Bank shooting attack on Friday that killed her daughters, aged 16 and 20.
The families were residents of Efrat, an illegal Jewish settlement in the West Bank.
Israeli police stormed the prayer hall of Jerusalem's Al-Aqsa mosque - Islam's third-holiest site - this week. This has become a regular occurrence during the holy month of Ramadan despite international status quo agreements.
Hundreds of Palestinians were detained and injured in the raids. In response, more than 30 rockets were fired from Lebanese soil into Israel.
Israeli forces said the attack was most likely carried out by the Palestinian armed movement Hamas.
Israel then bombarded the Gaza Strip and southern Lebanon, targeting what it called "terror infrastructures", belonging to Hamas.
"We will not allow the terrorist Hamas to establish itself in Lebanon", by acting on "all fronts", Netanyahu said at a news conference on Monday.
Israeli attacks on Palestinians have intensified since Netanyahu took power in December at the head of a coalition government which includes extreme-right and ultra-Orthodox Jewish parties.
The attack on the Al-Aqsa Mosque took place after Netanyahu announced a "pause" on a controversial judicial overhaul which split Israel, causing unprecedented protests and divisions within the government.
Among the political casualties was Yoav Gallant, whom the prime minister dismissed on March 26 after he called for a halt to the judicial changes, citing national security concerns and threats by reserve military personnel not to report for duty.
Netanyahu is currently battling very low levels of domestic popularity. A recent survey showed him likely to lose if an election were held now.
At his news conference, Netanyahu said he and 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," he added.
In Tel Aviv, several hundred protesters took to the streets to denounce the government and condemn the prime minister's speech, according to images broadcast by Israeli television.
Israel has occupied the West Bank since the 1967 Arab-Israeli War and hundreds of thousands of Jewish settlers live in Israeli-approved settlements which are considered illegal under international law.