From left, Secretary of State John Kerry, Israeli Justice Minister Tzipi Livni and chief Palestinian negotiator Saeb Erakat leave the West Wing of the White House in Washington, Tuesday, July 30, 2013, after a meeting with President Obama. President Barack Obama on Tuesday delicately waded into the first round of Middle East peace talks in years, meeting privately at the White House with lead negotiators for the Israeli and Palestinian delegations. Secretary of State John Kerry stands between Israel's Justice Minister and chief negotiator Tzipi Livni, right, and Palestinian chief negotiator Saeb Erekat, as they shake hands after the resumption of Israeli-Palestinian peace talks, Tuesday, July 30, 2013, at the State Department in Washington. Israel's Justice Minister and chief negotiator Tzipi Livni, left, looks towards Palestinian chief negotiator Saeb Erekat during statements to reporters after their meeting together with Secretary of State John Kerry on the resumption of Israeli-Palestinian peace talks, Tuesday, July 30, 2013, at the State Department in Washington. Secretary of State John Kerry stands with Israel's Justice Minister and chief negotiator Tzipi Livni, right, and Palestinian chief negotiator Saeb Erekat, after the resumption of Israeli-Palestinian peace talks, Tuesday, July 30, 2013, at the State Department in Washington. A Palestinian woman holds a poster of Ahmed Saadat, a leader of the Popular Front for the Liberation of Palestine, imprisoned by Israeli during a protest in the town of Nablus in the West Bank on Tuesday, July 30, 2013. PFLP supporters protested against the resumption of of the peace talks with Israel. Arabic on the poster reads, "wherever I am, we will always continue to be against Zionism, prisoner and friend Ahmed Saadat." (AP Photo/Nasser Ishtayeh) WASHINGTON (AP) - Pressing ahead in a new U.S.-backed push for Middle East peace, Israeli and Palestinian negotiators agreed Tuesday to meet again within two weeks to start substantive talks in hopes of reaching a long-elusive settlement within nine months. Speaking after the two sides wrapped up an initial two days of talks at the State Department and visited President Barack Obama at the White House, Secretary of State John Kerry said Israel and the Palestinians were committed to sustained and serious negotiations on the "core issues" that divide them. The next round will take place in either Israel or the Palestinian territories before mid-August, he said. Kerry said he was aware of the deep doubts surrounding the new peace effort and acknowledged that the road would be difficult. Yet, he said, "While I understand the skepticism, I don't share it. And I don't think we have time for it. All issues, including contentious disputes over the status of the territories and Jerusalem, are "on the table for negotiation, and they are on the table with one simple goal: a view to ending the conflict," Kerry said. The U.S. had already said the negotiations would continue for at least nine months - roughly until the end of April 2014 - but that had not been set as a timeframe for reaching a deal. Kerry and both sides agreed that neither would walk away from the talks or take actions that could disrupt them for that period, two senior U.S. officials said. The officials spoke on condition of anonymity because they weren't authorized to discuss diplomatic talks. However, the officials also said they expect that the Israelis, over U.S. objections, will continue constructing housing for Jewish settlers on land claimed by the Palestinians over the course of the negotiations, an indication the Palestinians are serious about dropping their longstanding demand for a settlement freeze before returning to talks. The officials said the U.S. believes the Palestinians also will not attempt to win further international recognition as a state until a peace deal is completed, an effort that one official likened to a potential "train wreck." Kerry said that Israel, which agreed on Sunday to release more than 100 Palestinian prisoners as a goodwill gesture, would also take unspecified steps in the coming days to ease harsh living conditions in the West Bank and Gaza. The two senior officials said those measures complement a $4 billion private sector economic program that Kerry is trying put in place to assist the Palestinians. After Tuesday's conclusion of preliminary talks, Kerry said, "I firmly believe the leaders, the negotiators and citizens invested in this effort can make peace for one simple reason: because they must." He said, "A viable two-state solution is the only way this conflict can end. And there is not much time to achieve it. Kerry said the negotiations, to be mediated on a day-to-day basis by his new Mideast peace envoy, Martin Indyk, would be cloaked in secrecy and that the parties had agreed that he would be the only person to comment on them. He quickly added that he would not comment on them now, leaving unclear the framework for the talks that he struggled for six months to get back on track. Despite the secrecy, the broad outlines of an agreement are well known: The Palestinians want a state based on the borders, with agreed land swaps, that existed before the 1967 war in which Israel seized east Jerusalem and occupied the West Bank and Gaza. Israel wants security assurances and a recognition that it is and will remain a Jewish state. Obama laid out those parameters as U.S. policy for any negotiations in a May 2011 speech, but neither the Israelis nor the Palestinians have publicly signed off on them. The two senior U.S. officials would not say if either side had even tacitly agreed to proceed on that basis. The main issues on the table for negotiation include security, borders, the status of Jerusalem, the fate of Palestinian refugees and water, all of which have been responsible for cratering multiple U.S.-brokered peace efforts over the past two decades. Earlier Tuesday, Obama and Vice President Joe Biden met with the lead negotiators - Israeli Justice Minister Tzipi Livni and senior Palestinian official Saeb Erekat - for about 30 minutes. White House spokesman Jay Carney said Obama called the meeting to "directly express his personal support for final status negotiations." Obama pledged full U.S. support to the process, Carney said. At the State Department ceremony later, Kerry was flanked by Livni and Erekat - who each spoke briefly about the need to resolve the longstanding conflict. "It's time for the Palestinian people to have an independent sovereign state of their own," said Erekat. It's time for the Palestinians to live in peace, freedom and dignity within their own independent, sovereign state. Livni allowed that she and Erekat had been involved in failed negotiations before, notably the Annapolis Process that President George W. Bush initiated in 2008, but she said this time could be different. "You know, Saeb," she said to Erekat, "we all spent some time in the negotiations room ... but we didn't complete our mission. And this is something that we need to do now, in these negotiations that we will launch today. And the opportunity has been created for us, for all of us, and we cannot afford to waste it. "I believe that history is not made by cynics; it is made by realists who are not afraid to dream," Livni added. Let us be these people.