JERUSALEM — A series of grisly Palestinian attacks that killed several Israeli civilians has prompted the government to take unprecedented security measures amid growing public debate over whether the specter of another Palestinian Intifada, or uprising, is on the horizon.

Israel’s prime minister vowed a “harsh offensive” to counter rising violence that has focused in recent weeks on Jerusalem’s most sensitive holy site sacred to both Muslims and Jews, in a series of so-called “lone wolf” Palestinian attacks against Israelis. On Sunday, Israel announced that Palestinians would be temporarily barred from Jerusalem’s Old City, the first time Israel has taken this step since it captured the Old City in the 1967 Mideast War.

The latest spike in violence comes at a time when many Palestinians no longer believe that statehood through negotiations with Israel is possible. Israeli commentators have raised the possibility of a third uprising, though Palestinian President Mahmoud Abbas has so far prevented major outbreaks of violence despite his growing friction with Israeli Prime Minister Benjamin Netanyahu.

Israel’s leading newspaper commentator, Nahum Barnea, called the recent violence the “Third Intifada,” referring to Palestinian uprisings in the 1980s and the early 2000s. “Not calling it by name allows the political and military establishment to evade, repress, shirk responsibility,” he wrote in the Yediot Ahronot newspaper.

But Hani al-Masri, a Palestinian political analyst, said it was not likely the start of a new uprising. “Intifada needs a leadership and the Palestinian political leadership is against it,” he said.

Netanyahu convened an emergency meeting of top security officials as soon as he returned to Israel Sunday afternoon from the U.S. Channel 10 TV reported that Netanyahu asked the meeting if a third Intifada is under way, and was answered in the negative.

After the meeting Netanyahu said he ordered “additional steps to deter terror and punish terrorists.” He said that includes “fast-tracking the razing of terrorists homes” and beefing up security in Jerusalem and the West Bank.