Hillary Clinton, the US secretary of state, has met President Shimon Peres in Israel, in one of a series of meetings planned with the country's leaders.
The pair spoke at a press conference in Jerusalem on Monday.
"Israel and the US have to be smart, creative, and courageous," Clinton said.
"We need to meet the challenges and pursue the goals we've established. No one knows it better than President Peres."
Clinton met Foreign Minister Avigdor Lieberman before her meeting with Peres, Israeli newspaper, Haaretz reported.
She is expected to meet Defence Minister Ehud Barak, and attend a dinner with Prime Minister Benjamin Netanyahu, the newspaper said.
Egypt's political upheaval is on the agenda, but other likely topics include Iran's nuclear programme and the Israeli-Palestinian peace process.
However, few diplomats expect any kind of breakthrough, ahead of the November US presidential election.
Making her first trip to Israel in 22 months, and only her fourth visit as secretary of state, Clinton's talks will focus first and foremost on the political transition in Egypt, where newly-elected President Mohamed Morsi took office two weeks ago.
The ouster of former Egyptian President Hosni Mubarak last year has raised questions among Israelis about whether Egypt, the first Arab nation to have made peace with Israel, will adhere to that treaty under the new democratic government.
Clinton flew to Israel from Egypt, where she held talks on Saturday with Morsi, a former Muslim Brotherhood leader, who told her Egypt will respect its international treaties.
She also saw Field Marshall Hussein Tantawi, head of the military council that took over after Mubarak was toppled, and is in power struggle with Morsi.
During her visit, Clinton urged Morsi to "assert the full authority" of his office and said the military should return to a "purely national security role".
Clinton's discussions with Morsi on Saturday focused on the domestic political deadlock and economic development. She pledged hundreds of millions of dollars in debt relief, private investment and job creation funds - money the US administration had earlier promised.
"I have come to Cairo to re-affirm the strong support of the United States for the Egyptian people and their democratic transition," Clinton said at a joint news conference with Mohammed Amr, the foreign minister.