The Israeli and Palestinian leaders, Binyamin Netanyahu and Mahmoud Abbas, met for the first day of direct talks in Washington yesterday and agreed that a peace deal could be achieved within a year.

George Mitchell, the White House envoy who joined the negotiations, said the two leaders decided to begin putting together a framework agreement on all major issues – such as borders, Jerusalem, Jewish settlements and security – that will "establish the fundamental compromises necessary" to flesh out a comprehensive peace deal.

Mitchell said Netanyahu and Abbas agreed to meet again in a fortnight in the Middle East and every two weeks after that. The US secretary of state, Hillary Clinton, and Mitchell will attend the first of those meetings on 14 September.

The negotiations are likely to face their first real test with the next round of talks coming just days before Israel's partial freeze on construction of Jewish settlements in the West Bank comes to an end.

Netanyahu has so far resisted US calls to renew the freeze, which the Palestinians see as a litmus test of the Israeli prime minister's intent.

Mitchell declined to disclose the detail of the discussions, although he said some of the major issues were touched on. Netanyahu and Abbas met US officials and then met privately. Mitchell described the two men's relationship at the talks as "cordial".

Before the talks opened, Netanyahu said two key demands – recognition of his country as a Jewish state and arrangements to ensure it does not come under attack from within a Palestinian state – were a prerequisite to a wider agreement.

Netanyahu again called Abbas his "partner in peace" and said he was prepared to make "painful concessions" to reach a deal. But the Israeli prime minister said that what he called the "two pillars to peace" must be resolved.

Clinton launched the negotiations by calling for the leaders to show themselves as bold and courageous statesmen and reach a comprehensive peace agreement within the one-year deadline set by Barack Obama. "We understand the suspicion and scepticism that so many feel born out of years of conflict and frustrated hopes," she said. "But by being here today you each have taken an important step toward freeing your peoples from the shackles of a history we cannot change."

Netanyahu said Israel was prepared to make sacrifices to reach an agreement. "Together we can lead our people to a historic future that can put an end to claims and to conflict. This will not be easy. A true peace, a lasting peace, will be achieved only with mutual and painful concessions from both sides … from my side and from your side," he said.

Hamas responded to the talks by announcing that it has joined forces with other armed groups such as Islamic Jihad to launch a wave of attacks against Israel. Earlier this week, Hamas claimed responsibility for the killing of four Jewish settlers in the West Bank, including a pregnant woman.

The Israeli prime minister said there were two issues that he regarded as central to any agreement: legitimacy and security. "Just as you expect us to be ready to recognise a Palestinian state as the nation state of the Palestinian people, we expect you to be prepared to recognise Israel as the nation state of the Jewish people," he said. "I said too, a real peace must take into account the genuine security needs of Israel … new forces have risen in our region, Iran and its proxies and the rise of missile warfare [with Hamas attacks from Gaza]. A peace agreement must take into account security arrangements against these real threats."

Abbas said he believed a deal was possible. "We're not starting from scratch, because we had many rounds of negotiations between the PLO and the Israeli government."