JERUSALEM, Israel -- U.S. Secretary of State John Kerry left Israel on Monday but is expected back next week.
His visits are part of a major U.S. effort to broker an agreement between Israelis and Palestinians.
Kerry says his efforts are not mission impossible.
"I will say that we are working with great intensity, with serious purpose, with the commitment to trying to resolve this conflict that has gone on for many years too long," he told reporters Saturday following a meeting with Palestinian President Mahmoud Abbas.
"Which I think presents us now with possibility of trying to find a framework agreement which would really lay out the end game, and lay out the framework for the major issues to guide the negotiations, from this point forward," he said.
Chief Palestinian negotiator Saeb Erekat agreed.
"What Secretary Kerry is doing, and let me reiterate in front of him, is not an interim agreement, not a transitional period. It's beyond that," Erekat said. "We're working hard to achieve an agreement on all core issues."
Those core issues include borders, security, and the fate of Jerusalem. One reported issue is the proposal that Israel give up the strategic Jordan Valley to the Palestinians.
Yet three U.S. senators, speaking at a Jerusalem press conference, warned recent history shows when Israel gives up land, it puts the Jewish state at risk.
For example, after Israel left Gaza in 2005, Hamas and other terror groups have fired thousands of rockets into Israel.
"Here's the one thing I think that dominates the thinking in Israel," Sen. Lindsey Graham,R-S.C., said. "Once you withdraw, then the ability to go back is almost impossible, once you give up your ability to kind of chart your own destiny. Look at Gaza. What's the chance of going back into Gaza militarily?"
Former Israeli Ambassador to the U.S. Danny Ayalon told CBN News he believes the agreement would base a future Palestinian state on the West Bank, including Jerusalem.
"I believe the deal that he offers is the '67 borders on the basis of '67 with swaps on a one-to-one ratio that would include Jerusalem as far as Kerry is concerned. This is what I believe. That would be for the Palestinians of Israel as a Jewish state," he said.
While Kerry puts U.S. prestige on the line to create a Palestinian state, some are concerned the Palestinians see the negotiations only as one stage in their long range plan.
Abba Zaik, a senior Palestinian official, told Syrian TV a Palestinian state based on the 1967 lines was only the beginning.
"Even the most extreme among us, Hamas, or the fighting forces, want a state within the '67 borders," he said. "Afterward, we [will] have something to say because the inspiring idea cannot be achieved all at once - rather in stages."
Many interpret the "inspiring idea" as the elimination of the state of Israel.