Mr. Netanyahu said the new measures would apply “to all citizens and residents of Israel” — a reference that includes the Palestinians of East Jerusalem, which Israel annexed after the 1967 war in a move that has never been internationally recognized. Most East Jerusalem Palestinians have not applied for Israeli citizenship but do hold permanent residency status.

East Jerusalem has erupted in waves of violence and confrontations with Israeli security forces over the last 15 months, beginning with the kidnapping and killing of a Palestinian youth, Muhammad Abu Khdeir, 16, by Jewish extremists who were acting to avenge the kidnapping and killing of three Jewish youths by Palestinians in the West Bank, according to the Israeli authorities. Tensions over a contested Jerusalem holy site have also flared into repeated bouts of violence, including in recent weeks.

The police have increased their presence in East Jerusalem and said that over the past 10 days they had arrested more than 130 Palestinians suspected of throwing rocks and firebombs, 61 of them minors.

Micky Rosenfeld, a spokesman for the Israeli police, said the .22-caliber bullets fired from Ruger rifles were not meant to be lethal and were “normally used in order to prevent and neutralize the immediate danger” in life-threatening situations. He described it as “a basic, simple means that can be effective in certain ranges.” The government statement said “relevant restrictions” would be applied to the use of live ammunition, without elaborating.

But B’tselem, an Israeli human rights organization, said that in the West Bank, which is under Israeli military rule, the use of the rifles was not likely to “have the result desired by the government.” Rather than restoring order to Jerusalem, the group said in a statement, it was likely to have lethal results and “exacerbate the cycle of violence.”

In some ways the new regulations blur the distinction Israel has always made between the occupied West Bank, where rights groups frequently accuse Israel of using excessive force, and annexed East Jerusalem, which Israel claims as part of its sovereign capital.

Nadeem Shehadeh, a lawyer for Adalah, an Arab civil rights group, said the proposed legislation for minimum sentences “goes against everything criminal law stands for.”