JERUSALEM — Despite an Israeli security crackdown that includes giving the police greater leeway to open fire and mobilizing 1,400 border police reserve officers, Israel is struggling to contain a spasm of violence.

Palestinians carried out four attacks against Israelis in Jerusalem on Monday alone.

In one, a 13-year-old Israeli boy in Pisgat Zeev, a Jewish area of East Jerusalem, was riding his bicycle when two Palestinians from a nearby neighborhood stabbed him, wounding him critically, according to the police. The assailants, cousins 13 and 15, also severely wounded a 25-year-old man.

The younger attacker was injured as he tried to flee, apparently hit by a car, according to the police. Officers fatally shot the elder one, the police said, when he charged at them with a knife and ignored calls to stop.

Two Israelis have been killed and more than 20 hurt in more than 15 knife attacks across the country just this month. About 10 Palestinians have been fatally shot by the security forces while they were carrying out, or attempting to carry out, attacks, or after snatching weapons from soldiers or police officers.