The last time Benjamin Netanyahu met an American president as Israel’s new leader, in 1996, it did not go well. Mr. Netanyahu lectured President Bill Clinton about Arab-Israeli relations, aides recalled, driving Mr. Clinton into a profane outburst after his guest left.

Mr. Netanyahu is likely to avoid a repeat of that when he meets President Obama at the White House on Monday. But the relationship between Israel and the United States has become more unsettled since Mr. Obama took office.

Israel has been rattled by signs that the Obama administration has sworn off the unstinting support of Israel that was a hallmark of the Bush years, as well as by the softer approach that Mr. Obama has taken to dealing with Iran.

Both countries regard Iran as the paramount threat in the region, but they have sharply different ways of responding: the Obama administration is asking for time to pursue its diplomatic overture to Tehran; the Israelis are warning that they will not stand by while the Iranians build a nuclear bomb.

Two weeks ago, the director of the Central Intelligence Agency, Leon E. Panetta, held a quiet meeting with Mr. Netanyahu in Jerusalem. Israel asked the United States to clarify benchmarks that would demonstrate that its diplomatic campaign was working.

The Israeli government, officials said, has assured the United States that it will not take military action against Iran without first consulting Washington. But it has also signaled that it will give the United States only a year or so to show that its good-will approach is getting results.

“They’re preoccupied by Iran, and no one more than the current prime minister,” said Martin S. Indyk, a former American ambassador to Israel and a Middle East peace negotiator. “But the prime minister understands full well that this is a time for American-led engagement.”

The question, Mr. Indyk said, is whether Mr. Netanyahu and Mr. Obama can find common ground on Iran. Without that, he said, it would be hard to imagine the Israeli government’s making progress on negotiations with either the Palestinians or its Arab neighbors.

“There is potential for greater tensions than have existed for some time, certainly,” said Robert Malley, another veteran of Middle East peacemaking efforts. “But a collision is not inevitable.”

To try to keep the peace process alive while it reaches out to Iran, the Obama administration has been pushing for a series of more modest steps on the part of Israel and its Arab neighbors.

The special envoy for the Middle East, former Senator George J. Mitchell, has made three trips to the region since January, seeking pledges from Saudi Arabia and other countries to exchange diplomats and authorize direct flights to Tel Aviv — steps that inch toward normalized relations. In return, he is pressing Israel to freeze the construction of Jewish settlements on the West Bank.

“The notion is that you can somehow induce the Arabs to give the Israelis an incentive,” said Aaron David Miller, a former diplomat who negotiated on Arab-Israeli issues in the Clinton administration.

Drawing in the Arab states, he said, is a way to reshape a forbidding landscape. In addition to Iran, there is a fractured Palestinian leadership and an Israeli government led by Mr. Netanyahu, who refuses to endorse the two-state solution that underpins the American-led peace effort.

Some analysts play down Mr. Netanyahu’s hawkish stance as a negotiating tactic ahead of his meeting with Mr. Obama. “I suspect he knows these are untenable conditions,” Mr. Malley said. “Those are concessions he’s putting himself in a position to make later.”

Despite Mr. Netanyahu’s rough start with Mr. Clinton, the two leaders later formed a productive relationship.

The Obama administration has fired its own warning shots. It asked Congress to make minor changes in a bill to allow aid to flow to a Palestinian unity government that would include members backed by Hamas — a step away from a blanket refusal to deal with Hamas, which it labels a terrorist organization.

The changes ruffled lawmakers in Congress, who tweaked the wording to make it more restrictive. But the episode rattled Israeli officials, who recently waged a fierce military campaign against Hamas in Gaza to stem its rocket attacks.

Adding to Israel’s qualms, a senior State Department official, Rose Gottemoeller, said at a recent conference in New York that the United States favored having Israel sign the Nuclear Nonproliferation Treaty, which would require it to declare and give up its nuclear arsenal.

While the administration said this was not a new policy, few American officials have publicly acknowledged that Israel possesses nuclear weapons, let alone raised the prospect of getting Israel to give them up. For the most part, though, the administration has moved gingerly. Mr. Mitchell, the president’s emissary to the Middle East, has yet to give an on-the-record interview about his diplomacy.

Diplomats are closely watching two other officials with long experience and strong views on Israel: the national security adviser, Gen. James L. Jones, and the White House chief of staff, Rahm Emanuel.

General Jones has made the case that if Israel believes that Iran is a threat to its existence, it should pursue talks with the Palestinians. Israeli officials, however, say they cannot do that unless they feel secure from the threat of an Iranian nuclear attack. And they fret that Iran is playing for time.

“They are making it too early to react until it is too late to react,” said a senior Israeli official, speaking on condition of anonymity because he did not want to interfere with Mr. Netanyahu’s visit.

Netanyahu Meets Jordan’s King

JERUSALEM — Prime Minister Benjamin Netanyahu of Israel met on Thursday with King Abdullah II of Jordan, who urged him to commit to a two-state solution with the Palestinians, according to news reports.

Mr. Netanyahu made the unannounced trip to Jordan hours before he was to meet with Pope Benedict XVI. Mark Regev, a spokesman for the prime minister, said that Mr. Netanyahu and King Abdullah discussed bilateral issues and the peace effort with the Palestinians.

A statement issued by Jordan after the meeting and quoted by news organizations said that the king had also asked Mr. Netanyahu to accept the Arab peace initiative, which offers Israel normal ties with the Arab world in return for a full withdrawal to its pre-1967 boundaries and a solution for the Palestinian refugees of 1948.