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Two Palestinians have been killed and 15 injured during an Israeli raid in the Jenin refugee camp in the occupied West Bank, Palestinian officials say.
The Israeli military said its troops responded to fire from Palestinian gunmen as they apprehended "terrorist suspects". One soldier was injured.
The raid came after a man from a nearby village killed five people in Israel.
Elsewhere in the West Bank on Thursday, an Israeli was stabbed and wounded by a Palestinian, who was then shot dead.
A total of 11 people have been killed in three attacks in Israel over the past two weeks, raising fears of what the country's prime minister has called "a wave of murderous terrorism".
The Israel Defense Forces (IDF) said soldiers and Border Police officers entered Jenin early on Thursday to make several arrests, including those of two people suspected of helping a local Palestinian man who shot dead five people in a suburb of the Israeli city of Tel Aviv on Tuesday evening.
"Palestinian gunmen opened fire at the soldiers, who responded with fire. One IDF soldier was injured and evacuated to a hospital for medical attention," the military tweeted.
The Palestinian health ministry said two young Palestinians - Sanad Abu Atiyeh, 17, and Yazid Saadi, 23 - died after being brought to local hospitals. Three of the injured Palestinians were reported to be in a critical condition, the ministry added.
In a separate incident, an Israeli civilian was stabbed and wounded by a Palestinian on a bus in the Gush Etzion settlement bloc, in the southern West Bank, the Israeli military said.
"Another civilian on the bus operated to thwart the attack and neutralised the terrorist," it added.
Israeli media reported that the injured civilian was a 28-year-old man and that he was in a serious condition in hospital after being stabbed in the upper body with a screwdriver. The Palestinian - identified as Nidal Jumaa Jaafr, 30, from the town of Tarqumiyah - was shot and killed, they said.
The BBC's Yolande Knell in Jerusalem says the latest violence suggests the continuation of a worrying trend in the run-up to a sensitive time when religious holidays will overlap for Muslims, Jews and Christians, putting pressure on Jerusalem's contested holy sites.
On Wednesday evening, Prime Minister Naftali Bennett said the IDF, the Israel Police and the Shin Bet security agency had "significantly increased their intelligence operations in order to reach, in a timely manner, those who are planning to carry out attacks".
"We have also reinforced the presence throughout the country of those in uniform and those carrying weapons."
But he also told Israeli citizens: "Whoever has a licence to carry a weapon, this is the time to carry it."
"This is neither our first nor our second wave of terrorism. We have experience with struggle. Israeli society, when it is tested, knows how to show composure, remain resilient and rise to the occasion. We cannot be broken," he added.
He spoke after funerals were held for two of the five people killed in Tuesday's attack in Bnei Brak, a predominantly ultra-Orthodox Jewish neighbourhood of Tel Aviv.
A Palestinian gunman opened fire at passers-by on residential streets, killing two Israeli civilians, as well as two Ukrainian men and an Israeli Arab police officer who confronted him at the scene. The gunman was shot dead by another officer.
Palestinian militant groups welcomed the attack. But it was condemned by President Mahmoud Abbas, who said it might lead to escalation at a time when "we are all striving for stability".
Israel was already on high alert after three Israeli Arabs linked to the Islamic State (IS) group carried out two attacks that left six people dead.
Four people were killed in a car-ramming and stabbing attack in the southern city of Beersheba on 22 March, and two police officers were shot dead in the coastal town of Hadera on Sunday. All three assailants were shot dead.