U.N. Secretary-General Ban Ki-moon led a chorus of voices expressing alarm of the escalation of the conflict in the Middle East.
"This must stop," he said in a statement.
At least 15 people were killed in Gaza as the Israeli military pounded the region Monday. Rockets fired from Hamas-controlled territory on southern Israel left three people dead and at least 79 wounded.
Carter, acting as a representative of The Elders, an international advocacy group founded by Nelson Mandela, said the region is headed to an outcome that "will fail to ensure the security and democratic rights of the people of Israel and renege on the promise of self-determination for Palestinians."
Both parties to the conflict are under pressure to find a peaceful solution to the crisis. Arab broadcaster al-Arabiya reports that both sides have agreed on a truce but differ on the best path toward implementation.
Members of The Elders said they spoke with regional, Israeli and Palestinian leaders in a two-day visit to the region.
"They urge a fresh, concerted approach to explore all alternatives to the current stalemate in negotiations, stressing that a two-state solution is the only realistic path to lasting peace in the Middle East," the organization said in a statement.
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