When Hillary Rodham Clinton ran for a New York Senate seat nine years ago, she labored to persuade skeptical Jewish voters of her support for Israel, after an incident in which she stood by as the wife of Yasir Arafat delivered an inflammatory attack on Israeli policies.

Now, having secured her standing as a friend of Israel, Mrs. Clinton must show a new audience that she can also be a mediator in her next expected role as secretary of state, when her first challenge may well be the renewed violence in Gaza. Given Mrs. Clinton’s once troubled history with Arab-Israeli issues, that could be a tricky task.

Mrs. Clinton brings several strengths, according to current and former aides and Middle East experts, including her knowledge of the region and experience in navigating it, as well as lingering good will among Arabs and Israelis won by her husband, Bill Clinton, for his efforts to broker a peace deal in the waning days of his presidency.

But Mrs. Clinton will have to reassure the Palestinians that she, too, can be a broker, working with Egypt and other Arab neighbors, and putting pressure on the Israeli government, when needed.

“She’s going to have to demonstrate her independence from Israel,” said Aaron David Miller, a public policy analyst at the Woodrow Wilson International Center for Scholars. “Our interests are inevitably going to diverge from their interests. We cannot be an ‘amen corner’ for them.”

The diplomatic tightrope was evident this week, as the departing secretary of state, Condoleezza Rice, condemned Hamas for firing rockets into southern Israel, while she privately urged Israeli leaders to agree to a cease-fire, after days of escalating airstrikes against Hamas militants in Gaza.

Mrs. Clinton has not commented on the latest violence; a spokesman said she would abide by the principle that “there is one secretary of state at a time.” But as New York’s junior senator, she strongly condemned a round of Hamas rocket attacks on Israeli towns in May 2007.

“I stand with the people of Israel who live in fear as their homes are besieged, and maintain my unwavering commitment to the welfare and survival of the state of Israel,” Mrs. Clinton said in a statement at the time.

In a speech to an Israeli lobbying group shortly after she lost the Democratic nomination to Barack Obama, Mrs. Clinton said the next president should shun direct negotiations with Hamas because it was a terrorist group, equipped by Iran and bent on destroying Israel.

Earlier, Mrs. Clinton declared that the United States could “obliterate” Iran if it attacked Israel with nuclear weapons — a far more strident tone than that of her potential new boss, President-elect Obama.

Most experts believe that Mrs. Clinton’s support of Israel is heartfelt, even if it is also smart politics in New York.

But when she was first lady, Mrs. Clinton made waves on two occasions for seeming to tilt toward Palestinian interests. In 1998, she told a gathering of Israeli and Arab teenagers that creating a state of Palestine was “very important for the broader goal of peace in the Middle East.”

The White House disavowed her comments, saying they did not reflect the administration’s policy. Today, the two-state solution is a central part of the American blueprint for a peace deal.

More trouble loomed in November 1999, when Mrs. Clinton, by then a Senate hopeful, visited the West Bank town of Ramallah. At a ceremony with Palestinian health officials, the first lady did not react when Suha Arafat accused Israeli forces of using “toxic gases” against Palestinians, causing cancer in women and children.

At the end of the ceremony, Mrs. Clinton gave Mrs. Arafat a polite kiss — a gesture that angered Jewish groups and earned the first lady critical newspaper editorials in New York.

Mrs. Clinton attributed her silence to the fact that the translation of Mrs. Arafat’s remarks was incomplete. An aide who was with her said Mrs. Arafat’s accusations appeared to be standard boilerplate, to those listening. The full import of her words set in only hours later.

The tempest briefly threatened Mrs. Clinton’s Senate bid in New York, though she managed to put it behind her through a fence-mending tour with Jewish leaders. After eight years of her steadfast support for Israel, the incident is viewed by most analysts as ancient history.

In one way, Mrs. Clinton’s baggage may carry a silver lining. Some Palestinians point out that she was ahead of the curve, as an American public figure, in calling for a Palestinian state.

Her marriage to former President Clinton also gives her a valuable calling card. Though his efforts to forge a peace deal fell apart, Middle East experts say that people on both sides credit him for trying longer and harder than other presidents.

“People don’t just perceive her as a senator from New York who was very close to Israel,” said Ziad J. Asali, the president of the American Task Force on Palestine, an Arab-American advocacy group that favors a Palestinian state. “They perceive her as a Clinton.”

Being a Clinton also gives the next secretary of state ready access to Mr. Clinton’s Middle East brain trust. Mrs. Clinton is being advised by Martin S. Indyk, who was a senior State Department official and United States ambassador to Israel during the Clinton administration.

Mr. Indyk is among those mentioned as a potential special envoy to the Middle East. Given the gravity of the crisis, however, experts say Mrs. Clinton may well have to tackle Gaza herself.

Some predict that Mrs. Clinton will be given the benefit of the doubt merely because she represents a new White House. While Mr. Obama’s response to the Israeli assault on Hamas has not differed much from that of President Bush, Mr. Asali said the Bush administration would bear the brunt of any anti-American feeling that bubbled up as a result of the attacks.

The challenge for Mrs. Clinton, experts said, will be reaffirming her support for Israel while establishing strong relations with Egypt, an undertaking many believe will be critical to brokering a durable cease-fire in Gaza.

“She has to quickly restore the relationship with Egypt,” said Mr. Miller, a former State Department veteran of numerous Middle East peace negotiations. “In doing so, she’s going to have to bear the brunt of being accused of indirect negotiations with Hamas.”

Given the pace and fluidity of events in the Middle East, some experts say that the Gaza crisis may end up as a footnote in Mrs. Clinton’s diplomatic tenure, even if it now looms as a huge early test.

“She may have to deal with a rough episode coming in, but it doesn’t have to define her,” said David Makovsky, a senior fellow at the Washington Institute for Near East Policy. “You need a smart person who understands the complexity of the situation, and she is that.”