JERUSALEM -- A suspected Palestinian attacker killed an Israeli woman and seriously wounded a man in the south of the occupied West Bank on Monday, Israeli authorities said, as violence flared in the restive territory two days after a shooting that killed two Israelis.

Elsewhere in the West Bank, an Israeli military raid triggered fighting with Palestinians south of Nablus, Palestinian health officials said, leaving eight Palestinians wounded -- including one in critical condition. Footage captured by witnesses from nearby buildings showed that an apparently unarmed Palestinian man was walking away from Israeli troops when he was shot in the back of the head. Israel's paramilitary border police said they were investigating the incident.

Monday's violence was part of a sharp escalation in recent months involving Palestinian militants, Israeli security forces and radical Jewish settlers. It took place as Israeli forces were already on high alert and searching for the gunman who had killed two Israelis in the northern West Bank on Saturday.

The combustible mix of armed Palestinians carrying out shooting attacks as well as near-nightly -- and often deadly -- raids by the Israeli army to arrest militants has fuelled the worst fighting in the West Bank in nearly two decades.

Reprisals by Jewish settlers against Palestinians have also heightened tensions. Late on Sunday, Israeli settlers threw stones and firebombs at a Palestinian home south of Nablus near the site of Saturday's deadly attack, local officials reported, causing damage but no injuries.

On Monday, a Palestinian gunman opened fire at an Israeli car on Route 60, the main north-south road in the West Bank, near the Palestinian city of Hebron. The army said the apparent drive-by shooting killed an Israeli woman and seriously wounded a man.

Prime Minister Benjamin Netanyahu visited the scene of the attacks shortly afterward. He warned Israel was "in the grips of a new terror offensive."

"We are working around the clock -- all of the officers and soldiers -- in order to apprehend the killers," he said.

The victims' sedan was riddled with over a dozen bullet holes. The gunman fled, prompting Israeli forces to conduct their second large-scale search in as many days. The military shut down all entrances to Hebron along with other towns to the south and east.

An offshoot of the secular nationalist Fatah party, the Al Aqsa Martyrs' Brigade, claimed responsibility for the attack, calling it a "natural response to the crimes of the occupation."

"For killing there is killing, for bombing there is bombing, for terror there is terror," it said.

The Israeli rescue service reported that the two victims were in their 40s and that a 6-year-old girl who was also in the car was unharmed. The man was taken to a hospital, the rescue service said.

A regional council representing settlements identified the woman killed as Batsheva Nigri, a mother of three and a kindergarten teacher, who lived in the Jewish settlement of Beit Hagai, near Hebron.

Meanwhile in the Gaza Strip hundreds of Palestinians protested near the Israeli border, throwing rocks and explosive devices at the fortified border fence. Israeli forces responded with tear gas and live fire, wounding 18 people, according to the enclave's health ministry.

Monday's shooting came two days after another Palestinian attack killed an Israeli father and son who were getting their car washed in the northern Palestinian town of Hawara, putting the West Bank on edge.

As Israeli forces stormed into nearby towns to conduct searches Monday, dozens of Palestinians flooded the streets to protest. In the town of Beita, south of Nablus, Palestinians hurled rocks and bricks at Israeli troops, said Israel's border police, a paramilitary arm of the Israeli police that operates on the West Bank, in parts of Jerusalem and in other volatile settings. As the protest escalated "so did the level of response by the security forces," it said.

The border police also said they were reviewing cases of Palestinians being hit by live fire, including the incident caught on camera showing a Palestinian shot and critically wounded while walking away and posing no apparent threat to troops. Palestinian media identified the man as Ameed Jaghuob, a local electrician.

Nearly 180 Palestinians have been killed by Israeli fire in the West Bank since the start of this year, according to a tally by The Associated Press. Israel says most of the Palestinians killed were militants. But stone throwing youths protesting the incursions and those not involved in the confrontations have also been killed.

Some 30 people have been killed by Palestinian attacks against Israelis during that time.

Israel says the raids are meant to dismantle militant networks and thwart future attacks. Palestinians say the raids undermine their security forces, inspire more militancy and entrench Israeli control over lands they seek for a hoped-for future state. Israel captured the West Bank in the 1967 Mideast war, along with east Jerusalem and the Gaza Strip.