In remarks to high-school seniors heading for compulsory military service, he spoke of the role of Palestinian teenagers in the unrest that erupted in early October.
"When there's a 13-year-old girl holding scissors or a knife and there is some distance between her and the soldiers, I don't want to see a soldier open fire and empty his magazine at a girl like that, even if she is committing a very serious act," Lieutenant General Gadi Eisenkot said in remarks broadcast today by Israel's private Channel Two television.
Since October 1, Palestinian knife, gun and car-ramming attacks have taken the lives of 25 Israelis, an American and an Eritrean, according to an AFP count.
At the same time, 160 Palestinians have been killed by Israeli forces, most while carrying out attacks but others during clashes and demonstrations.
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A disturbing number of attackers have been young teenagers. Israel's Yediot Aharonot newspaper quoted what it said was an internal study document by the army and the Shin Bet domestic security service which said 37 percent of them were aged between 16 and 20.
In October, 15-year-old Hassan Mansara was shot dead by security forces after stabbing and seriously wounding two Israeli schoolboys in annexed east Jerusalem.
His accomplice and cousin Ahmed, 13, was hit by a car as he fled, hospitalised and later charged with attempted murder.
The following month, in an incident to which Eisenkot may have been alluding, two Palestinian girls aged 14 and 16 stabbed with scissors and lightly wounded an elderly man in Jerusalem.
Police opened fire, killing the 16-year-old and seriously wounding the 14-year-old.
Swedish Foreign Minister Margot Wallstrom enraged Israel in December when she called on Israel to halt what she called "extrajudicial executions" in response to attacks.