The appeal came during a meeting in the West Bank with Palestinian President Mahmoud Abbas, a rare face-to-face encounter after a more than yearlong diplomatic standstill.
Officials on both sides said that Abbas initiated the meeting with Isaac Herzog, leader of the opposition Zionist Union, in response to the violence of recent weeks.
Addressing reporters at Abbas' West Bank headquarters in Ramallah, Herzog said the two men held an "in-depth" discussion that lasted more than an hour.
"We have agreed that in order to prevent a third intifada we must combat terror on the one hand aggressively, and on the other hand move toward a diplomatic process," he said. "We must ignite the process yet again and give it another effort."
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After the meeting, Herzog wrote on his Facebook page that he believed a deal could be reached within two years if there was sufficient political will.
For now, the odds of bringing Abbas and Israeli Prime Minister Benjamin Netanyahu together for a meeting much less restarting peace talks appear virtually nonexistent.
The U.S. Is not expected to resume peace efforts until after a congressional vote on the international community's Iranian nuclear deal. Netanyahu bitterly opposes the deal, and with U.S.-Israel ties suffering, the prospects for any new U.S. Diplomatic initiative seem poor.
Even if the U.S. Manages to restart talks, the gaps between the Israeli and Palestinian leaders are so vast that a deal is unlikely. The Palestinians seek the West Bank, east Jerusalem and Gaza territories captured by Israel in 1967 for a future state. Netanyahu opposes a return to Israel's pre-1967 lines and rejects any withdrawal from east Jerusalem, the Palestinians' hoped-for capital. The area is home to key Jewish, Muslim and Christian holy sites.