US Secretary of State John Kerry was meeting Israeli Prime Minister Benjamin Netanyahu for the third time in 24 hours on Friday for talks understood to be focused on security.
Kerry, who is seeking ways to drive forward stagnant peace talks, met twice with Netanyahu on Thursday for more than six hours of talks about potential security issues in any peace agreement.
He also held a three-hour meeting in Ramallah with Palestinian president Mahmud Abbas.
On Friday, Kerry met Israeli Finance Minister Yair Lapid at a Jerusalem hotel before entering another round of talks with Netanyahu, officials said.
The US diplomat was then expected to head straight to Ben Gurion airport near Tel Aviv where he would hold a news conference before flying home.
Kerry has said Israel's security is "fundamental" to the peace negotiations with the Palestinians, and a top priority for Washington in nuclear negotiations with Iran.
But his talks in Ramallah did not appear to go so well, with a senior official saying US proposals on security were unacceptable.
"Today, we discussed at great length issues of security in the region, security for the state of Israel, security for a future Palestine. And we, I think, made some progress," said Kerry.
"The interests are very similar, but there are questions of sovereignty, questions of respect and dignity which are obviously significant to the Palestinians, and for the Israelis -- very serious questions of security," he said.
Chief negotiator Saeb Erakat told AFP the situation was "still very difficult and matters are complicated" but another senior Palestinian source was more direct, saying Kerry's security proposals "were very bad ideas which we cannot accept".
In talks with Netanyahu on Thursday, Kerry and top security adviser General John Allen outlined their view of some of the security challenges likely to face Israel in the context of a final peace agreement.
Maariv newspaper said Israeli officials were pleased with Kerry's security proposals, but firm opposition from the Palestinians was what prompted him to schedule a third meeting with Netanyahu.
A diplomatic source quoted by the paper said Washington "had moved considerably in the direction of Israel's demands" and had "accepted Israel's position on a long-term presence in the Jordan Valley".
The outline "gives good answers to the Israeli demands and is very forthcoming towards Israel," the source said.
Earlier this week, Haaretz newspaper said Washington was focusing on resolving Israel's security needs in the hope it would allow them to push Netanyahu on other aspects, such as the borders of a future Palestinian state.
Netanyahu has said Israel would only accept the emergence of a Palestinian state if it was demilitarised, with Israeli troops deployed along the Jordan Valley -- an option the Palestinians completely reject.