The two sides also met with Qaurtet Representative Tony Blair and the Quartet Envoys from the European Union, the United States, Russia and United Nations.
Jordan's King Abdullah II has implored Israel and Palestinians to resume peace talks and hosted Tuesday’s meetings.
The Jordanian Foreign Minister, Nasser Judeh, said the talks were held in a positive atmosphere. Although there were no breakthroughs on matters of "substance," he said, "the important thing is the two sides have met face to face."
Mr Judeh voiced cautious optimism. "The two sides expressed their commitment to a two-state solution. We do not want to raise the level of expectations, but at the same time we do not want to minimize the importance of this meeting.
"The Palestinians submitted a paper on borders and security. The Israeli side received it, promising to study it and respond.
"We agreed that the discussions will be continuous," he said, "and will take place here in Jordan."
The Israelis and Palestinians agreed to send their chief negotiators to Jordan under pressure from the Quartet.
The Quartet has been working for months to restart peace talks in accordance with the Quartet statement that was agreed at the United Nations in September.
A diplomat who attended the larger meeting told the Associated Press that the talks were "serious."
"It was a brainstorming session in which both sides, the Israelis and Palestinians, showed eagerness to restart peace negotiations," the diplomat said.
At the United Nations, Secretary-General Ban Ki-moon welcomed Tuesday's talks. "The secretary-general encourages the parties to build on this meeting and to continue working to establish forward momentum toward a lasting peace," said a statement issued by his office.
"The next meeting is now on Monday the 9th," State Department spokeswoman Victoria Nuland said, confirming they will take place in the Jordanian capital Amman, as did a first round of talks earlier this week.
"The good news here is we do appear to be in a process where the parties will be meeting directly, and we hope that this will continue even beyond Monday the 9th," Nuland said.