(CNN) -- Secretary of State John Kerry met with Israeli Prime Minister Benjamin Netanyahu for more than three hours in Jerusalem on Friday as he pushed a new framework for a peace deal between Israel and the Palestinians.
The meeting was private, but earlier in the day, three Republican senators who also met with Netanyahu shared some of Israel's concerns.
Netanyahu named two major concerns, Sen. Lindsey Graham of South Carolina told reporters. One is the threat of a nuclear Iran, and the other is the marginalization of Israel by Palestinians going outside of the peace talks and directly to the United Nations to seek statehood.
Graham, who was accompanied by Sens. John McCain of Arizona and John Barrasso of Wyoming, said they shared the prime minister's concerns.
The trio of Republicans said they support a lasting peace process, but not one that puts Israel at a disadvantage.
Kerry arrived in Tel Aviv on Thursday and immediately headed for Jerusalem, the start of his ninth trip to the region since taking over as America's top diplomat nearly a year ago.
At the outset of the trip, he said that the time is close for tough decision-making.
A senior State Department official said Kerry's talks with Netanyahu and Palestinian President Mahmoud Abbas would be substantive.
"It is an effort to provide agreed guidelines for a permanent status agreement; that is to say, a full and final peace treaty between the parties," the official said.
Kerry's proposal is based on five months of intensive consultations with Israelis and Palestinians since the resumption of the peace process last summer. As a result of those talks, he intends to test some of his ideas with the two leaders.
CNN's Elise Labott contributed to this report.