Mrs Clinton expressed "unrelenting" commitment to Israel's security
US Secretary of State Hillary Clinton has restated "unshakeable" support for Israel, whatever type of government emerges from current coalition talks.
Mrs Clinton is on her first visit to the region as the top diplomat of Barack Obama's US administration.
Right-winger Benjamin Netanyahu, who opposes some key US policies, has been asked to form Israel's next government.
Mrs Clinton also announced two senior US officials would head for Syria, Israel's long-time foe, for talks.
"We are going to be sending two officials to Syria. There are a number of issues that we have between Syria and the US, as well as the larger regional concerns that Syria obviously poses," Mrs Clinton said.
Syria had engaged in indirect negotiations with the outgoing Israeli government on the fate of the Israeli-occupied Golan Heights.
The US has kept Damascus at arms length for several years, accusing it of supporting terrorist groups and destabilising its Arab neighbours.
However, analysts say recent diplomatic moves could be a prelude to restoring a US ambassador in Damascus.
Mrs Clinton arrived in Israel from Egypt, where the US and other international donors pledged almost $4.5bn (£3.2bn) for rebuilding Gaza.
I know this is a sensitive time in Israeli politics as the process of forming a new government unfolds. This is a matter for the Israeli people
She has held talks in Jerusalem with the mainly ceremonial president, Shimon Peres, before going on for a meeting with outgoing Foreign Minister Tzipi Livni.
She is also due to meet Mr Netanyahu and the caretaker Prime Minister Ehud Olmert.
On Wednesday, she will enter the West Bank for more talks Palestinian Authority President Mahmoud Abbas, who was present Monday's Egyptian-hosted aid conference in Sharm el-Sheikh.
Hillary Clinton: 'This is a sensitive time in Israeli politics'
After meeting Mr Peres, Mrs Clinton said it was important to underscore the "unshakeable, durable and fundamental" US support for the state of Israel… [and] our "unrelenting commitment to Israel's security".
"We will work with the government of Israel that represents the democratic will of the people of Israel," Mrs Clinton said.
Mrs Clinton has repeatedly said the new US administration is committed to the establishment of a Palestinian state as the best way to end the Israeli-Palestinian conflict.
Mr Netanyahu has not endorsed this view, and he campaigned on pledges to concentrate on economic development of the Palestinian territories, which were occupied by Israel in the 1967 war, rather than political deals.
"I know this is a sensitive time in Israeli politics as the process of forming a new government unfolds. This is a matter for the Israeli people to decide under Israeli law," she added.
The BBC's Middle East correspondent Tim Franks says the relationship between the US and Israel may become a little less warm than it was under the Bush administration.
American diplomacy may sound a new tone with stronger condemnation of Israeli settlement building in the West Bank, as well as greater pragmatism in dealing with the reality of Hamas's control of the Gaza Strip, he adds.
During Mrs Clinton's visit, Israeli warplanes bombed smuggling tunnels on the border between Gaza and Egypt, injuring six people according to Palestinian medical sources.
On Monday, a rocket was fired from the Gaza Strip at the city of Ashkelon. There were no reports of injury or damage.
Also on Monday, the Israeli government lodged an official complaint with the United Nations about the continued rocket fire from Gaza.
"The government of Israel will continue to safeguard its citizens and will do everything in its power to ensure that the situation in the south will not go back to what it was before December 2008," the letter read.
"Israel will not endure and will respond in kind to attacks against its citizens."
The Israeli military says 130 rockets and mortars have been fired from Gaza since each side adopted unilateral ceasefires in January.
Israel has launched a series of bombing raids on alleged arms smuggling operations and has kept tight curbs on the entry of goods into the heavily-populated coastal strip.
Israel launched a major military offensive on Gaza in December and January, in which about 1,300 Palestinians were killed, of whom 412 were children, and which destroyed thousands of homes and businesses. Thirteen Israelis were killed during the three weeks of violence.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.