JERUSALEM — Nearly four years ago, when Senator Barack Obama was running for president and Prime Minister Benjamin Netanyahu of Israel was head of the opposition, they met here in what aides described as a warm atmosphere.

President Obama and Prime Minister Benjamin Netanyahu, in the Oval Office last July, will meet again on Monday.

“Senator,” Mr. Netanyahu said to Mr. Obama, “as president, many things will cross your desk, but the most important, by far, will be stopping Iran from obtaining nuclear weapons.”

On Monday, the two will meet again in the shadow of an American presidential election, and Iran will again dominate the conversation. But the bonhomie will be replaced by wary intrigue as Mr. Netanyahu and Mr. Obama try to sort out their differences, in timing, messaging and strategic bottom lines, on how to grapple with Iran — while also managing their own strained relationship.

Mr. Netanyahu, who will address Aipac, the American Israel Public Affairs Committee, right after his White House meeting, is hoping to prompt more clarity from Mr. Obama on how he sees increasingly tough sanctions and diplomacy with Iran playing out in the coming months.

He also wants to press Mr. Obama on where his red line lies: how and when the United States will decide whether sanctions are succeeding or failing, and how committed he is to the use of force, officials and analysts following the discussions on both sides said in recent days.

For Mr. Obama, the challenge is to deliver two competing messages. He wants to join Mr. Netanyahu in warning Iran to abandon its nuclear program or face military action, but also to press him to give time to sanctions and diplomacy and hold back his military.

“This is being billed as the most important encounter ever between the two,” said Abraham H. Foxman, national director of the Anti-Defamation League and a prominent Jewish leader. “Both of them need success here. There has to be a serious understanding, there has to be real trust, and so far I don’t think it’s there.”

Much has divided the two leaders in the eight previous meetings they have held during the three years they have been in power, especially what Israel should do to promote peace with the Palestinians, including stopping settlement construction in the occupied West Bank.

But with the region in turmoil and the Palestinian peace talks frozen, the central concern the two men are facing is the Iranian nuclear program.

The talks are complicated, especially for Mr. Obama, by domestic politics. Israel’s security and the Iranian nuclear program have drawn the most attention of any foreign matters in the Republican primaries. That leaves Mr. Obama with somewhat less room to maneuver than he would have at another moment in his presidency. The men will meet the day before the Super Tuesday nominating contests in 10 states.

“Whether they say it or not, both will be influenced by their own domestic politics,” said Zalman Shoval, a former Israeli ambassador to Washington who presides over an advisory group for Mr. Netanyahu on American-Israeli relations. “Public opinion polls in America are about 50-50 on whether America should take a role in an eventual military operation against Iran. This is not the main element in a decision, but it will have some influence on the candidate, who happens to be president.”

Some argue, therefore, that if Mr. Netanyahu decides to attack Iran’s nuclear facilities, he is more likely to do so before the November election, figuring Mr. Obama would find his hand forced into at least tacitly supporting the move.

But others make two counterarguments. The first is that Mr. Netanyahu believes that Mr. Obama is likely to be re-elected and does not want to alienate him. The second is that no matter who is in the Oval Office, Israel will not outsource what it views as its vital security interests based on an American promise to take military action if sanctions fail. Israel’s goal is an American attack on Iran, but it seems unlikely to wait till it no longer can do it by itself.

This is because the red lines that Israel and the United States draw regarding Iran have been in different places.

For Israel, it is Iran’s capacity to build a nuclear weapon quickly; whereas for Washington it is the actual building of the weapon. Moreover, the American military has more, better and more sophisticated equipment so it can attack at a later date and still be effective even if Iran’s enrichment facilities have been moved underground beyond Israel’s reach.

All of this is making for complex calculations on both sides. If Mr. Obama trusted Mr. Netanyahu more, he might issue a more muscular statement of military threat to Iran, confident that Israel would not move too quickly without coordination. And if Mr. Netanyahu trusted Mr. Obama more, he would be less jumpy over every statement of caution emerging from Washington, like one by Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff, that it would not be prudent to decide to attack Iran now because it would destabilize the region.
Five Republican senators were in Israel recently and met with Mr. Netanyahu. Senator John McCain of Arizona told reporters afterward that “there is clearly significant tension that now exists on how to approach this whole issue,” adding, “There should be no daylight between America and Israel in our assessment of the threat.”

Thomas E. Donilon, Mr. Obama’s national security adviser, also spent two days here recently, along with a team of intelligence and defense officials, meeting with Mr. Netanyahu and his lieutenants. Both sides contended that the meetings were highly successful. The Israelis were told that the administration not only says it would use military force if sanctions against Iran failed, it is also doing the planning for it.

Still, Mr. Netanyahu and several of those closest to him doubt that Mr. Obama would ultimately take military action against Iran. Others in Israel, including Defense Minister Ehud Barak, are more persuaded by Mr. Obama’s assurances.

Sallai Meridor, a former Israeli ambassador to Washington, reflected a widespread Israeli view that the world has done little to block unstable countries from obtaining nuclear weapons.

“Look at the record,” he said. “Pakistan was allowed to go nuclear. I don’t think anyone thought that was a good idea. One can assume that if Israel didn’t do what it did in 1981, Iraq would have been allowed to go nuclear. Then imagine the 1990 gulf crisis.”

Even some Israeli officials who believe that Mr. Obama would use force say they cannot wait until an attack is beyond their abilities. If Israel, in a nod to allowing sanctions and diplomacy to work, allows Iran to get past the point where it can effectively strike, it will have handed over its fate to the United States. While it would like Washington to strike, it does not want to wait past its own abilities, because even an ironclad promise of action could prove fickle.

When Mr. Netanyahu spoke to Aipac two years ago, he invoked World War II and two of the past century’s greatest statesmen to make a point about self-reliance, a point that his staff applies to Mr. Obama.

“Seventy-five years ago, the leading powers in the world put their heads in the sand,” Mr. Netanyahu said then. “Untold millions died in the war that followed. Ultimately, two of history’s greatest leaders helped turn the tide. Franklin Delano Roosevelt and Winston Churchill helped save the world. But they were too late to save six million of my own people. The future of the Jewish state can never depend on the good will of even the greatest of men.”