Editor's note: Jonathan Schanzer is vice president at Foundation for Defense of Democracies, where Grant Rumley is a research analyst focusing on Palestinian politics. The views expressed are their own.
(CNN) -- Early on Tuesday morning, two Palestinian men from the East Jerusalem neighborhood of Jabel Mukaber entered a synagogue in the sleepy West Jerusalem neighborhood of Har Nof and went on a killing spree. Armed with guns and knives, the two men killed four rabbis -- three Israeli-American and one Israeli-British -- before they were struck down by Israeli police. The attack, which also claimed the life of a police officer, was the deadliest in a series of recent "lone wolf" attacks against Israelis across Jerusalem.
The Israeli response was swift. The Israeli military ordered the demolition of the perpetrators' homes. Israeli border police blocked access to several East Jerusalem neighborhoods that have been recent flash points for conflict. And Israeli security services conducted raids in several towns in the West Bank.
Israeli Prime Minister Benjamin Netanyahu condemned the attacks and hammered Palestinian leader Mahmoud Abbas for inciting the ongoing violence in Jerusalem. Similarly, U.S. Secretary of State John Kerry condemned the "senseless brutality," and called on Abbas to do the same.
Abbas soon stepped up. It was his first condemnation of any attack in Jerusalem since the unrest began last month. Indeed, the aging Palestinian leader is walking a tightrope. On the one hand, lone wolves are by definition not under the control of Abbas nor other Palestinian political organizations. And it is also true that Abbas has not been the driving force of the Jerusalem unrest. But at the same time, he does appear to be making an effort to benefit from the tensions, seemingly seeking to ride this current wave of nationalist fervor.
Yet Abbas is also operating from a political place of strength. The West trusts him because he brought an end to the violence of the second intifada, or uprising (2000-2005). The Israelis need him because his forces in the West Bank cooperate with the Israelis on a range of security issues. In many ways, Abbas is responsible for preventing a third intifada in the West Bank -- the territory he controls.
However, both Israel and the United States have badly mismanaged the relationship with the Palestinian Authority, doubling down on a system that has failed to invest in Palestinian good governance, let alone new leadership. As a result, neither have much leverage to tone down his rhetoric, short of threatening to oust him from power.
Ultimately, though, there is also the question of whether the Palestinian leader actually has the ability to bring stability back to Jerusalem. Even though Palestinians claim the city as their capital, Jerusalem is outside of Abbas' jurisdiction. Moreover, Abbas is now nine years into a four-year term, and his popularity is flagging.
The 79-year-old Abbas may be thinking about his legacy after nearly a decade of failed peace talks and internecine squabbles that have divided the Palestinian people, both politically and geographically. The key question is whether Abbas believes he can resuscitate his political fortunes on the Palestinian street by supporting the Jerusalem unrest. If he does, the path to de-escalation is clouded.
If Abbas is not the answer, the trick for U.S. and Israeli policymakers is identifying who else to engage. And it is far from clear who that person might be.