Palestinian president Mahmud Abbas said on Tuesday opportunities to resume peace talks with Israel should be seized, but played down prospects for success.

"We will keep coordinating with King Abdullah II, and we welcome any chances provided by Jordan to back peace efforts," Abbas said after meeting the monarch in Amman, according to a palace statement.

"Any chance must be taken advantage of, no matter how weak hopes are," he added, a day after Israeli and Palestinian negotiators held a second meeting in a week to find a way to get back to peace talks following more than 15 months.

Abbas expressed hopes that the two sides will meet on January 26 "to refer to the legal foundation that allows them to return to negotiations."

The date was set by the diplomatic Quartet of the United States, United Nations, European Union and Russia for both parties to present their proposals on borders and security with an eye to resuming direct talks shortly afterwards.

"At our second meeting today we continued our efforts to explore the positions of both parties to resume the negotiations," a Palestinian official close to the Amman talks told AFP on Monday.

The first round of the talks were held in Amman last Tuesday between Palestinian negotiator Saeb Erakat and Israeli envoy Yitzhak Molcho. Those talks were described as positive.