The Israeli and Palestinian negotiators will meet again within two weeks in either Israel or the Palestinian territories to continue peace talks, US Secretary of State John Kerry said on Tuesday following the initial round of talks in Washington.Kerry, speaking with the Israeli and Palestinian negotiators at his side, declared that the parties in the historic conflict had agreed to hold "sustained, continuous and substantive" conversations on all issues requiring resolution for a final peace agreement.Reuters contributed to this report.He said this week's round of talks between the two sides were positive and constructive and he was convinced that they could make peace.The first round of negotiations lasted through Monday night and Tuesday morning, and included bilateral discussions between the direct parties as well as talks with the Americans, including US special envoy to the peace process Martin Indyk, Secretary Kerry and President Barack Obama himself, who hosted the two parties at the White House with Vice President Joseph Biden in attendance.Kerry said the parties had agreed that the only solution the conflict is the implementation of a two-state solution, with both states given assurances of peace, security and mutual recognition."We cannot pass along to another generation the responsibility of ending a conflict that is in our power to resolve in our time," Kerry said.The secretary of state stressed that all final status, core issues were on the table for the talks.He reiterated the need for both sides to make "reasonable compromises," saying both Israel and the Palestinians would stand to gain from such compromises.He added that both parties are already making concessions, and called for an end "once and for all to the pernicious attacks on Israel's legitimacy."Kerry also noted that the content of the meetings will be kept confidential, and that he is the only one authorized to make any public comments to the press on the talks.He cautioned against putting much stock in any other media reports on the talks.The secretary of state added that as a part of building mutual trust, the Israeli government will take a number of steps to improve the conditions in the West Bank and the Gaza Strip. He noted that Palestinian security forces were recognizing these steps, which has led to increase in law and order and a decrease in terrorism in the Palestinian territories.Chief Palestinian negotiator Saeb Erekat said that he is "delighted that all final status issues are on the table to be resolved," and said the time has come for peace for the Palestinian people.He stated that the Palestinians have suffered enough, and that no one benefits more from the success of this endeavor.Israeli negotiator and Justice Minister Tzipi Livni thanked both Kerry and US President Obama for their commitment to the peace talks and determination to ensure their success.Livni stated Israel is hopeful for the talks, but cannot afford to be naive.She praised Netanyahu and his cabinet for demonstrating "courage" and conviction in supporting the resumption of negotiations with concrete sacrifices.She also assured that Israel has no intention to argue about the past, it instead wishes to create solutions and make decisions about the future.Finally, she expressed hope that the resumption of negotiations can cause a spark of hope to emerge from cynicism and pessimism. "Our job is to transform this spark of hope to something real and lasting. Peace is not made by cynics, but by realists who are not afraid," she said.Livni had to leave Washington for a vote in Israel, ending talks for the time being, the State Department said.Following the briefing, the Middle East Quartet, consisting of the United Nations, Russian Federation, United States and European Union, put out a statement in support of Kerry. "While noting that much hard work lies ahead, the Quartet expresses its hope that renewed negotiations will be substantive and continuous and set a clear path towards a two-state solution, the end of conflict, and lasting peace and security for both Israelis and Palestinians," the statement read. "The Quartet intends to meet soon at the Envoys level to discuss next steps."Israeli ambassador to the US Michael Oren and his Palestinian counterpart Maen Areikat were in attendance.