After a meeting that lasted more than three hours in Amman, Jordan, Palestinian negotiator Saeb Erekat and Prime Minister Benjamin Netanyahu's envoy Yitzhak Molcho agreed on Tuesday to meet again next week in the Jordanian capital.

Want updates on the latest in Mideast peace talks? Join Haaretz.com's Facebook page

Jordanian Foreign Minister Nasser Judeh, who hosted the meeting, said the first face-to-face Israeli-Palestinian meeting in more than 15 months had been "positive."

Speaking in a press conference following the meeting, Judeh said that all the core issues of a future peace deal were discussed in the meeting, saying that "the Palestinian side presented its positions concerning borders and security and the Israeli side heard them and promised to go over them in the next few days."

The Jordanian FM added that more meetings will take place in the coming days, some of which will be known to the public and some of which will remain secret.

The Palestinian positions concerning borders and security arrangements were given to the Israeli representative in two separate documents, representing the first time an Israeli representative ever accepted to receive Palestinian documents concerning the final borders of a future Palestinian state under PM Netanyahu.

For his side, the Israeli representative to the talks gave both Erekat and the Quartet and Jordanian envoys a overview of points which Israel considers as essential in any future agreement.

Molcho specified in he would present an Israeli document responding to the one handed by the Palestinians that would too deal with borders and security arrangements.

The low expectations which led up to the Erekat-Molcho meeting apparently caused all involved, including Jordanian and Quartet representatives, to consider it as "good and constructive."

The meeting began at 5 P.M. local time, with Molcho and Erekat sitting at both ends of the table along with Judeh, Quartet Mideast envoy Tony Blait and senior U.S., Russian, UN, and EU diplomats.

After a meeting of about an hour the Quartet representatives left the room, leaving only the Israeli and Palestinian representatives along with the Jordanian FM, who later met each of the envoys in person. After about three-and-a-half hours the session was adjourned.

State Department spokeswoman Victoria Nuland remarked on Tuesday's meeting, indicating that the January 26 Quartet deadline was not as much of an issue as long as the parties continued negotiations.

"What's most important is that these parties are talking, we want to see what the results are before we get ourselves too formalistic here", she said, adding that the U.S. was "seeking to have them meet face to face, and we were encouraging them to make concrete proposals to each other."

"What we want to see is where the parties came out after this round. We are very grateful to Jordan and particularly to Foreign Minister Judeh for bringing the parties together not only to meet with the Quartet envoys as they have been doing, but also to meet with each other in a face-to-face meeting," Nuland added.

Nuland also reiterated U.S. policy on settlements, sayying: "You know where we've been on settlement activity. You know where we've been on housing activity in Jerusalem. None of this is helpful. None of it contributes to peace. That said, the best way to end up with borders that are agreed and understood is for these parties to talk to each other and to come up with a settlement together."

Earlier on Tuesday, Palestinian President Mahmoud Abbas threatened to take “new measures” against Israel attempts to renew Mideast peace talks fail.

Mr. Abbas said that if Israel accepts the Palestinian conditions, “we will go to negotiations.” He said the Palestinians have set a Jan. 26 deadline for talks to resume. “After that date, we will take new measures. These measures might be hard,” he said.

In September, the Quartet set forth a four-month target for the sides to present proposals on the key issues of future borders and security arrangements. The Palestinians believe the timeline expires on Jan. 26. Israel says the clock doesn’t start ticking until negotiations are under way.