WASHINGTON, Jan 5 (Reuters) - Israeli and Palestinian peace negotiators will hold their second round of face-to-face talks within a week on Monday in Amman, a U.S. State Department spokeswoman said on Thursday.

We are encouraged that they are both coming to the table, they are talking directly, spokeswoman Victoria Nuland told reporters in her daily briefing.

The two sides held their first high-level talks in more than a year in Amman on Tuesday, a gathering sponsored by the Quartet of Middle East peace mediators -- the European Union, Russia, the United Nations and the United States.

The Quartet on Sept. 23 called for the two sides to resume talks with the aim of reaching a peace deal by the end of 2012.

Tuesday's talks did not produce any breakthroughs. They were aimed at agreeing to terms under which the two sides' leaders - Palestinian President Mahmoud Abbas and Israeli Prime Minister Benjamin Netanyahu - could resume talks.

Nuland said the next round was to be held in Amman and was expected to follow the format of Tuesday's meeting, which was attended by Palestinian negotiator Saeb Erekat and Israel's Yitzhak Molcho.

The major issues dividing the two sides include the borders of a Palestinian state, the fate of Jewish settlements on the West Bank, the status of Jerusalem and the fate of Palestinian refugees. (Reporting by Arshad Mohammed; Editing by Bill Trott)