Jerusalem (CNN) -- Palestinian negotiators put forward proposals on security and borders during talks with Israeli representatives in Jordan, Palestinian media reported Tuesday.
Israel's special envoy, attorney Yitzhak Molcho, and chief Palestinian negotiator Saeb Erakat met in Amman with representatives of the Middle East Quartet -- made up of the United States, the European Union, the United Nations and Russia -- in an effort to relaunch negotiations after more than a year of deadlock.
Jordanian Foreign Minister Nasser Judeh told reporters that "serious and constructive talks" had taken place, the official Palestinian Authority news agency WAFA said.
He said the talks focused on the two-state solution, according to the Jordanian state news agency Petra.
The Israelis said they would consider the Palestinian proposals, and the two sides agreed to meet again in Jordan, the agency cited Judeh as saying.
However, no significant breakthrough was made, Judeh acknowledged. "The gap is wide between the two sides on all issues," he is quoted as saying by WAFA. "The issues are complicated and we do not expect to resolve them in a day or two."
Petra quoted Judeh as saying, "We don't want to raise the expectations about this meeting and we don't want to underestimate its importance in the same time."
Peace talks between Israel and the Palestinians fell apart more than a year ago over disagreements on the issue of Israeli settlements in the West Bank.
In September, Palestinian Authority President Mahmoud Abbas made a bid for the United Nations to recognize a Palestinian state, a move Israel called premature without direct talks to address its long-standing security concerns.
Filling the vacuum created by the removal of Egypt's former President Hosni Mubarak, Jordan's King Abdullah has taken a more active role in trying to bridge the gulf between Israelis and Palestinians.
In November, King Abdullah made a rare visit to the Palestinian political capital of Ramallah in the West Bank, followed by a meeting in Amman a week later with Israeli President Shimon Peres.
The United States has voiced its support for the new initiative.
"We are hopeful that this direct exchange can help move us forward on the pathway proposed by the Quartet," Hillary Clinton, the U.S. secretary of state, said Sunday night in a statement. "The status quo is not sustainable and the parties must act boldly to advance the cause of peace."
But while both sides thanked the Jordanian government for its role in bringing about the meeting, few expected any serious breakthroughs.
Speaking to Voice of Palestine radio beforehand, Erakat said the meeting would not constitute the resumption of negotiations, but rather would be one that could lead to the restarting of talks.
Former Quartet participant and American diplomat Robert Danin wrote Sunday for the Council on Foreign Relations that, while the resumption of contacts between the two sides would be a positive development, it "inadvertently makes the situation on the ground riskier."
"Abbas is returning to talks without attaining his long-standing demand that negotiations resume with an Israeli settlement freeze," Danin wrote. "Unless he can demonstrate quickly that talks produce tangible benefits for the Palestinians, he will feel compelled to break them off."
This, Danin said, could add impetus to Abbas concluding ongoing talks with Hamas about forming a Palestinian unity government -- an idea vehemently opposed by representatives of Israel and the United States, who consider the Islamist group a terrorist organization.
Sami Abu Zuhri, a spokesman for Hamas, said Monday he was surprised by the meetings. He said Hamas considered them a repetition of a failed initiative and called on the Palestinian Authority to cancel the meeting Tuesday with Israeli representatives.
Hamas spokesman Fawzi Barhoum told CNN that the meeting of the Palestinians with the Israeli occupying forces "is a mockery." Israeli government spokesman Mark Regev told CNN last week that "if Mahmoud Abbas walks toward Hamas, he is walking away from peace."
CNN's Kevin Flower contributed to this report.