Netanyahu and Kerry met at David's Citadel Hotel in Jerusalem on Tuesday morning, after "very productive" dinner talks late on Monday.
- Are Israel, PA finally set to resume peace talks?
- Kerry: Israel-Palestinian peace 'not easy, but possible'
- Op-ed: Settlements not main issue
"I think it's fair to say we made progress," Kerry said adding that movement in areas such as the economy "could be critical to changing perceptions and realities on the ground, all of which can contribute to forward momentum."
The two leaders had agreed "to do some homework" over the next few weeks "with a view to seeing how we can really pull all of the pieces together," he told reporters, praising Netanyahu for his "good faith efforts".
Kerry, Netanyahu: 'To do some homework' (Photo: Yonatan Zendel, Flash90)
"I'm determined not only to resume the peace process with the Palestinians, but to make a serious effort to end this conflict once and for all," Netanyahu said.
According to reports, Kerry was hoping to get Israel and the Palestinians to sit down in Amman for four-way talks with the United States and Jordan.
Secuirty concerns top Israeli agenda (Photo: Kobi Gideon, GPO)
The Al-Quds daily said Jordan was to be involved as a key player in negotiations over the status of Jerusalem, which Israel claims as its capital while the Palestinians want the annexed eastern sector as capital of their future state.
There was no immediate confirmation of either report, but Jordan has been a key player in the peace process since it signed a peace treaty with Israel in 1994.
Momentum is also gathering among Arab nations to revive the stalled peace process, with a delegation from the Arab League's Arab Peace Initiative (API) committee to visit Washington later this month.
The delegation includes the head of the Arab League's Arab Peace Initiative committee, Qatar's foreign minister, Hamad bin Jassim, Secretary General of the Arab League, Nabil al-Arabi, and the foreign ministers of Egypt, Saudi Arabia, Jordan, Morocco and the Palestinian Athourty.
During the meeting, Abbas told Kerry the release of prisoners held by Israel was a "top priority" for resuming peace talks, his spokesperson said.
Abbas also wants Netanyahu to present a map of the borders of a future Palestinian state before talks can resume.
The Palestinian leader has repeatedly made clear there would be no return to negotiations without a settlement freeze, but he has also made it known he would suspend for two months all efforts to seek international recognition of a Palestinian state to give US-brokered efforts a chance.
Roi Kais and AFP contributed to this report
- Receive Ynetnews updates
directly to your desktop