"They have courageously recognized that in order for Israelis and Palestinians to live together side by side in peace and security, they must begin by sitting at the table together in direct talks."
Kerry thanked Jordan's King Abdullah and Foreign Minister Nasr Judeh for their help during his visit, as well as the Arab League for its support of the peace initiative.
King Abdullah arrived in Cairo on Saturday to brief Egyptian officials about the agreement reached between the Palestinians and Israel on resuming peace talks, Jordan's royal court press office said.
His visit is the first to Egypt by a foreign head of state since the July 3 ousting of former Egyptian President Mohamed Morsy.
Meanwhile, Israel Defense Forces and the U.S. European Command are scheduled to hold a bilateral aerial exercise Sunday by both of their air forces, Israeli officials said. The regularly scheduled exercises will last about two weeks.
'Right for our future'
Israeli Justice Minister Tzipi Livni lauded the prospect of peace.
"These past few months were long, filled with doubt and cynicism," Livni said in a statement Friday. "But now, four years of political stagnation are coming to an end.
"I know that, despite this being an opportunity, once the negotiations begin they will be complex -- but I am convinced with all my heart that this is the right thing for our future, our security, our economy and Israel's values."
She expressed respect for Netanyahu "for making the decisions representing Israel's important interests, as well for American Secretary of State, John Kerry, which led us and the Palestinians into the negotiations room."
In the Palestinian territory of Gaza, however, Hamas dismissed the renewed effort for peace talks.
"This negotiation will be useless. It is not going to achieve anything for the Palestinian people. It will not help the prisoner issue, the border issue or the land issue," the group said in a statement. Israel imposed an economic blockade on Gaza shortly after Hamas was elected to run its government in 2006.
Talks based on land swaps, pre-1967 borders?
Kerry urged people to wait for all the elements of the agreement to be formalized, rather than guess at the detail.
"Any speculation or reports you may read in the media ... are conjecture ... because the people who know the facts are not talking about them," he said.
One of the reports Kerry may have been referencing was a Reuters report quoting an Israeli official who said the Jewish state agreed to a plan for peace talks based on pre-1967 borders and land swaps.
It would be in line with a decades-old United Nations resolution calling on Israel to release territories it gained during a war, a demand that Israel has historically fought. But it would help create contiguous borders for a future Palestinian state that would coexist next to a Jewish state.
Israel's official reaction to the report has been denial.