Talks were halted a year ago over the war in the Gaza Strip and have not resumed, due largely to a Palestinian demand that Israel first impose a complete freeze on building in the West Bank and East Jerusalem and Israel's refusal to do so.
The United States is making a fresh push to resolve the six-decade conflict, which U.S. officials believe destabilizes the region and fuels anti-American sentiment around the world.
George Mitchell, the US envoy for Middle East peace, travels to Europe next week and then to the region later in the month to see how it might be possible to restart talks.
US and regional officials have said the United States is looking at what assurances it might provide the Palestinians and Israelis -- possibly in the form of letters -- that might help the parties get back to the table.
Clinton did not squarely address the issue of letters but said that ending the dispute would require "guarantees and assistance" from the United States and others.
She also repeated recent US statements that address the Palestinian desire for a peace deal based on borders prior to the 1967 war in which Israel occupied the West Bank, and the Israeli desire to retain major West Bank settlement blocs.
Clinton said she could envisage an accord that "reconciles the Palestinian goal of an independent and viable state based on the 1967 lines with agreed swaps, and the Israeli goal of a Jewish state with secure ... borders that reflect subsequent developments and meet Israeli security requirements."
After meeting with Judeh, who said negotiations must be "bound by a timeline," Clinton held talks with Ahmed Aboul Gheit, the Egyptian foreign minister, who said he hoped to "create enough momentum" to get peace talks going again.