Israeli forces on Sunday hunted a Palestinian suspected of killing an 18-year-old military policewoman in east Jerusalem, an attack that left another Israeli in critical condition from a gunshot wound to the head.

The Saturday shooting at a checkpoint by the Palestinian refugee camp of Shuafat in Israeli-annexed east Jerusalem came amid spiralling violence in the Israeli-Palestinian conflict.

Hours earlier, two Palestinian teenagers were shot dead in an Israeli raid in the West Bank, as the United Nations warned of "mounting violence" in the occupied Palestinian territory.

Police said the alleged Shuafat gunman, a 22-year-old Palestinian resident of east Jerusalem, was driven to the checkpoint by an accomplice. He got out of the car, opened fire and ran into the camp as the driver sped away.

The dead Israeli soldier was identified as Noa Lazar.

Prime Minister Yair Lapid said Sunday his heart was "broken" by her death.

"We won't rest until bringing the despicable murderers to justice," Lapid said before Israeli Jews were set to mark the Sukkot holiday.

Another Israeli, a 30-year-old man, was taken to Hadassah hospital in serious condition after being shot in the head, the medical centre said in a statement.

Israeli police said shrapnel lightly wounded two additional border officers.

Israeli armed forces chief Lieutenant General Aviv Kohavi visited the checkpoint on Sunday.

A court meanwhile extended the detention by a week of four people arrested on suspicion of involvement in the attack, police said.

- Camp entrances shut -
 

As the pursuit of the gunman got underway, Israeli forces shut the entrances to the refugee camp.

The Palestinian Red Crescent Society said its medics were prevented from reaching the area, while the Israeli rights group HaMoked pressed officials to reopen access for thousands of residents "who need to get to their homes, work, school, and to hospitals".

Police on Sunday said officers were using "riot control weapons" in the camp, as dozens of people hurled stones at the force.

Smoke billowed from the densely populated neighbourhood.

Earlier Saturday, two Palestinian teenagers were shot dead in an operation by Israeli forces in Jenin, the northern West Bank flashpoint city.

The Palestinian health ministry announced the killing of "two citizens by occupation (Israeli) bullets in Jenin", while 11 others were wounded.

The ministry identified those killed as Ahmad Daraghmeh, 16, and Mahmud as-Sous, 18. The Islamic Jihad militant group praised the teenagers as "its martyrs".

Israel's military said troops had entered Jenin to detain a 25-year-old Palestinian it said was a member of Islamic Jihad and suspected of shooting at troops in the area.

"Dozens of Palestinians hurled explosive devices and Molotov cocktails at IDF (Israeli military) soldiers and shots were fired at them," an army statement said.

In response to attacks on Israeli civilians earlier this year, Israel's army has been conducting near daily raids in the West Bank that have left dozens dead, including Palestinian fighters and civilians.

- 'Deteriorating situation' -
 

Following the latest deaths in Jenin, the Palestinian presidency said Israeli action could "push matters towards an explosion".

"A point of no return, which will have devastating consequences for all", said Nabil Abu Rudeineh, spokesman for president Mahmud Abbas, in a statement published by the official Palestinian news agency Wafa.

The agency also reported Israeli forces had fired directly at journalists during the Jenin raid.

Two reporters were wounded Wednesday while covering a military operation witnessed by an AFP journalist near the West Bank city of Nablus, in which one Palestinian was killed.

In May, Palestinian-American journalist Shireen Abu Akleh was shot dead while covering an Israeli raid in Jenin.

Saturday's violence in Jenin came a day after Israeli forces shot dead two other Palestinian teenagers in the West Bank.

The UN envoy for Middle East Peace, Tor Wennesland, voiced alarm at "the deteriorating security situation", saying at least 100 Palestinians had been killed in the West Bank this year.

Israel has occupied the West Bank since the 1967 Six-Day War and around 475,000 Israelis now live in settlements across the territory, which are considered illegal by most of the international community.

They live alongside some 2.8 million Palestinians, who in different areas of the West Bank are subject to Israeli military rule or live under limited Palestinian governance.