Jordan's King Abdullah II on Tuesday met separately with Palestinian President Mahmoud Abbas and Middle East envoy Tony Blair to discuss the first Palestinian-Israeli meetings in more than 15 months to try to restart peace talks.

The discussions came ahead of the monarch's trip to the United States next week for talks with U.S. President Barack Obama, which will focus on efforts to resume the peace talks.

Palestinian chief negotiator Saeb Erekat and Israeli envoy Isaac Molho held a second meeting in Amman on Monday, but failed to achieve a breakthrough.

"There was a frank discussion, but the rift persisted when the parties came to handle important issues," Foreign Ministry spokesman Mohammad Kayed said, referring to the major stumbling blocks of borders and security.

"We have to exploit all chances, albeit they are weak, to push forward the peace process," Abbas told reporters, adding that a third meeting would be held on January 26.

During his meeting with Blair, who represents the Quartet of peace mediators - the United States, Russia, European Union and the United Nations - King Abdullah called for an intensified effort to resume peace negotiations aimed at establishing a Palestinian state.