At the same time, Clinton said she would not dictate orders to Israel, saying the Jewish state would determine its interests. In her first visit to the region as secretary of state, she also pledged "unrelenting" support for Israel's security.
Prime minister-designate Benjamin Netanyahu opposes Palestinian statehood and has been critical of peace talks. But after meeting Clinton, he said the two had "found a common language."
At a joint news conference with Foreign Minister Tzipi Livni earlier in the day, Clinton also said the U.S. would soon send two envoys to Syria for "preliminary conversations." It was the most significant sign yet that the Obama administration is ready to mend relations with the Damascus regime. The U.S. withdrew its ambassador in 2005, accusing Syria of supporting terrorism.
"We have no way to predict what the future with our relations concerning Syria might be," Clinton said. "There has to be some perceived benefit of doing so for the United States and our allies and our shared values."
Clinton lamented that President Barack Obama's attempts to reach out to Syrian ally Iran have so far been unsuccessful. The U.S. and Israel accuse Iran of pursuing nuclear weapons and supporting anti-Israel militant groups.
Clinton, seeking to calm her Israeli hosts, said diplomacy should not be confused with softness.
"When we talk about engagement with Iran, do not be in any way confused, our goal remains the same: to dissuade and prevent Iran from acquiring nuclear weapons and continuing to fund terrorism," she said. "Whatever we do will be done thoughtfully in consultation with our friends and Israel, most particularly Israel."
Senior Israeli officials, including Defense Minister Ehud Barak, told Clinton that Israel does not oppose Washington's overtures to Iran. However, they said they were skeptical about Iran's intentions and urged the U.S. to set a deadline for Iran to respond positively. Israel fears Iran will use American engagement to buy time to develop nuclear weapons.
When asked about Netanyahu, she acknowledged the possibility of disagreements with any Israeli government and made clear the U.S. will push forward with its efforts to forge a peace deal that includes the creation of an independent Palestinian state alongside Israel.
"The United States will be vigorously engaged in the pursuit of a two-state solution every step of the way," she said. "The inevitability of working toward a two state-solution is inescapable."
Netanyahu characterized his talks with Clinton as "deep and important and good" and said the two agreed to meet again once a new Israeli government is formed.
Netanyahu, leader of the hardline Likud Party, is putting together a new coalition government after right-wing and Orthodox Jewish parties won a majority of seats in last month's Israeli parliamentary election. He is expected to be sworn in as prime minister within weeks.
His criticism of U.S.-led Mideast peace talks during the recent election campaign has raised fears that his government could clash with the Obama administration.
But ahead of his meeting with Clinton, Netanyahu showed signs of backing off his previous pledges to abandon the current round of peace talks, launched in November 2007 at a U.S.-hosted summit.
That message would mark a change in the Likud leader's long-stated position that peace talks are a waste of time because of the weakness of the Palestinian leadership. He has suggested in the past he would instead invest in the Palestinian economy while continuing Israel's military occupation of the West Bank indefinitely.
"The common goal is creative thinking to get out of the maze and try to create a new reality," Netanyahu told journalists after his session with Clinton. "There is a deep will on both our sides to work in cooperation."
Several Netanyahu aides said his talks with Clinton focused on Iran and the Gaza situation. The aides said Netanyahu asked that the U.S. set a deadline for Iran to respond to its diplomatic overtures, but he did not say what the U.S. should do if the deadline passes.
They spoke on condition of anonymity because they did not sit in on the meeting, but instead had been briefed by Netanyahu.
Hamas officials reacted harshly to Clinton's criticism.
"We haven't seen anything good," said Fawzi Barhoum, a Hamas spokesman in Gaza. "She approves of occupation and its crimes and interferes in Palestinian internal affairs."
In Damascus, the U.S. Embassy announced that Jeffrey Feltman, the State Department's top diplomat for the Middle East, would lead the American delegation headed to the Syrian capital. Embassy spokeswoman Katherine Vandevate said the visit aims to build on his "substantive and constructive" meeting last month with Syria's ambassador in Washington, Imad Moustapha.
Clinton's packed schedule of meetings with Israeli leaders also included talks with Prime Minister Ehud Olmert. On Wednesday, she is to call on Palestinian President Mahmoud Abbas in the West Bank.