WASHINGTON — Heralding what he called a “new moment of possibility” toward Middle East peace, Secretary of State John Kerry on Tuesday announced an ambitious schedule for resolving the Israeli-Palestinian conflict, saying he hopes negotiators for the two sides will have agreed to a framework for a settlement in nine months.

President Obama put the weight of the White House behind the effort, personally greeting Israeli Justice Minister Tzipi Livni and chief Palestinian negotiator Saeb Erekat, who were in Washington for the first direct talks between the two sides in three years.

Kerry, too, has paid close attention to reviving the long-stalled process, and many now feel its success or failure will be a major part of his legacy. He’s traveled frequently to the region in the past four months, laying the groundwork. Overseeing the day-to-day progress will fall to special envoy Martin Indyk, who was named to the job on Monday.

Kerry conceded that pitfalls remain, but he said it wasn’t the time to listen to the skeptics who wonder how this plan will succeed when all such past attempts have collapsed. This time, at least, the talks appear to have made it to the next round – the parties have agreed to meet again in the Middle East within two weeks.

Livni and Erekat, along with their entourages, met with their U.S. counterparts Monday night for a brief round of introductory talks, followed by an Iftar, the traditional breaking of the fast in the Islamic holy month of Ramadan.