"No one should take the law into their own hands," said Israeli Prime Minister Benjamin Netanyahu.
He added that police were examining security tapes in attempts to identify those who assaulted the wounded man at a bus station in the southern city of Beersheba.
In the attack, an Israeli Bedouin Arab attacker killed a 19-year-old soldier, Omri Levy, whose military rifle was taken and used by the assailant. A second victim, police said, was an Eritrean asylum seeker shot by a security guard who mistakenly believed he was a second attacker.
In an apparent reflection of soaring tensions after weeks of violence and bloodshed in Israel, the wounded Eritrean was kicked and beaten by an Israeli mob as he lay bleeding. A few people dropped a line of bus station seats on the man. Others placed a chair above him as crowds closed in.
The attack, in the Negev desert city's central bus station during rush hour, follows more than two weeks of daily attacks by Palestinians against Israelis that has left the country shaken and suspicious.
Israel's Internal Security Agency identified the Beersheba attacker as Mohind al-Okbi, 21, a resident of a nearby Bedouin town. Some Bedouins in Israel serve as trackers in the Israeli military but many identify with the Palestinians, sharing the same religion, language and other cultural traits.
According to Israeli security services, most of the attacks were carried out by solo assailants not related to any militant Palestinian factions. Many of the attackers were teenagers and the majority have taken place in Jerusalem.