At least five unarmed young Palestinians, including a 21-year-old woman, have been shot dead by Israeli soldiers in 13 days since the start of the year, prompting mounting concern about the unwarranted use of live fire. A sixth was killed on his 17th birthday last month, and a seventh death this month is disputed by the Israeli military.

The commander of the Israeli Defence Forces (IDF) in the West Bank, Brigadier-General Hagai Mordechai has ordered all commanders to reiterate to all soldiers the rules of engagement, a military spokesman told the Guardian.

The use of live fire is permitted only in extreme circumstances, and shooting to kill only in a life-threatening situation. "None of [the dead] posed a threat that justifies the use of lethal force," said Sarit Michaeli, of the Israeli human rights organisation B'Tselem and the author of a report published on Monday which analyses the IDF's use of crowd control weapons in the West Bank. "Swift action by the army is required to transmit a clear message to soldiers that the lives of Palestinians have equal value and that firing live ammunition in non-life threatening situations is illegal."

The youngest to be killed was 15-year-old Salah Amarin, who died last Wednesday, five days after being shot in the head during clashes near Aida refugee camp in Bethlehem. According to the IDF, he had been launching stones from a slingshot.

The same day as Amarin died, Lubna al-Hanash, 22, was shot in the face while walking on a college campus south of Bethlehem. According to the IDF, a routine patrol in the area had opened fire in self-defence after being "confronted by Palestinians with Molotov cocktails". But Suad Jaara, a friend who was injured in the shooting, told the Palestinian news agency Ma'an: "An Israeli soldier was shooting from his rifle while a white car was parked on the roadside. There was no one in the area except Lubna and I."

Sixteen-year-old Samir Awad was shot on 15 January after crossing a fence that forms part of the security barrier near his home in the village of Budrus. He had just completed school exam before a midterm break from school when he was grabbed by soldiers, broke free and ran away. Soldiers opened fire, hitting him from behind in the back and the head. The IDF said Awad was "attempting to infiltrate into Israel".

Three days earlier, Uday Darwish, 21, was also shot in the back while running away from soldiers after attempting to cross the separation barrier south of Hebron, according to Palestinian sources. The IDF said "soldiers at the scene fired towards his legs".

Last month, Mohammed al-Salaymeh was killed by a female soldier at a checkpoint in Hebron while en route to buy a cake to celebrate his 17th birthday. The IDF said he had brandished a toy gun. Grainy video footage of the incident appears to show the youth struggling with a soldier, and then being shot three times. The third and final shot is fired as Salaymeh is leaving the scene.

In Gaza, Anwar al-Mamlouk, 19, was shot in the abdomen 50 metres from the border fence on 11 January by Israeli soldiers, according to the Palestinian Centre for Human Rights.

Three days later, a 21-year-old farmer, Mustafa Abu Jarad died after being shot in the head. The IDF denied it was responsible.

According to B'Tselem, IDF regulations say live fire is permissible "in a case of violent rioting by the separation barrier, when there appears to be a real threat of damage to, or breaching of, the barrier, and when less severe methods have proved to be ineffective, the commander of the force may, as a last resort, authorise the firing of single shots of live ammunition at the legs of those people identified as central agitators".

At least 46 Palestinians have been killed since 2005 by live ammunition fired by soldiers at stone-throwers, says its report, Israel's Use of Crowd Control Weapons in the West Bank. The most common crowd control weapons are tear gas, rubber-coated bullets, stun grenades and "skunk" – the use of foul-smelling liquid in water cannon.

"Live ammunition is the most lethal means used by security forces at West Bank demonstrations," says the report. "The Israeli military's standing orders explicitly state that live ammunition may not be fired at stone-throwers."

The IDF said the report relied on "a biased narrative" and "specific incidents … are exceptions to IDF policy rather than the rule". It added: "Every soldier who is expected to contend with these situations regularly trains with riot dispersal means and is carefully taught the rules of engagement."

The Palestinian prime minister Salam Fayyad called for "strong condemnation from the international community" of the recent spate of deaths from live fire, and urged "immediate intervention to compel Israel to desist from these serious attacks on our people".

The UN special co-ordinator for the Middle East peace process, Robert Serry, has also raised concerns about the use of live fire by Israeli soldiers in the West Bank.

In an editorial published before the most recent two deaths, the liberal daily Haaretz said the "basic problem emerging from these cases … is in soldiers and commanders' overly-free interpretation regarding the circumstances permitting killing Palestinian civilians who only approach the fence, or even try to cross it, without endangering the lives of Israeli soldiers or civilians."

It added: "The consecutive incidents in which Palestinians were killed in recent days give the feeling that Palestinian blood may be shed with impunity."

• This article was amended on Monday 28 January 2013 to correct a typographical error in the headline.