For all the fears of an outbreak of fighting in the Middle East that could draw the United States, Israel and Iran into direct combat, a curious feature of the conflict so far is the care taken — in both Tehran and Washington — to avoid putting their forces into direct contact.

No one knows how long that will last, American and European diplomats and other officials say. But 100 days into the conflict, the assessment of most of the key players is that Iran has pushed its proxies to make trouble for the American military and to pressure Israel and the West in Iraq, Syria, Lebanon and the shipping lanes of the Red Sea while going to some lengths to avoid provoking a larger eruption.

It is the most delicate of dances, rife with subtle signals, attacks and feints, and deniable action. The evidence of caution is piecemeal, but everywhere.

While Tehran has ramped up its production of uranium drastically in recent weeks, renewing fears that it may be speeding again toward the capability of fabricating several nuclear weapons, it has carefully kept just below the threshold for bomb-grade fuel. That is considered the red line that could trigger military action against its underground nuclear complexes.

When Israel struck a suburb of Beirut on Jan. 2 to kill a Hamas leader, it mounted a very precise attack — exactly the opposite of its campaign in Gaza — to avoid harm to nearby Hezbollah fighters. That allowed Israeli officials to make clear to Hezbollah, the terrorist group funded and armed by Iran, that it had no interest in escalating the tit-for-tat strikes on Lebanon’s southern border. (Six days later it did kill Wissam Hassan Tawil, a commander of Hezbollah’s most elite force, the most senior Hezbollah officer killed thus far.)

And when the United States took out Houthi launching facilities, radar and weapons depots in Yemen several days ago, it struck at night, after clearly telegraphing its intentions, and avoided targeting the Houthi leadership behind the attacks on shipping in the Red Sea.

However happy Iranian leaders may be to stir the pot in the Middle East, all-out war is not in the interests of a country whose supreme leader is in poor health and whose streets have been filled with protesters in recent years. What the Iranian leadership cares about the most is “regime stability,’’ said Ryan C. Crocker, a former U.S. diplomat.

The United States, too, has tried to keep the fighting contained.

But history is replete with failed efforts to keep American troops out of conflicts half a world away that were spinning out control, as was made clear by the U.S. entry into World War I in 1917, World War II in 1941, Korea in 1950 and Vietnam, gradually, in the 1960s. Accidents, assassinations, sinking ships and guidance systems gone awry can all undermine the most carefully planned strategy.

Yet in Ukraine, nearly two years in, a similar, unspoken set of restraints has worked — somewhat to the amazement of even President Biden’s closest aides. Early on, Mr. Biden directed the military to do anything it could to support Ukraine — as long as American forces did not take on Russia’s directly, whether on land, in the air or on the Black Sea. He also mandated that Ukrainians not use American weapons against targets inside Russian territory, though there remains a constant worry about what will happen if a Russian missile hits a neighboring NATO country.

But Moscow and Washington had a nearly 80-year history of Cold War signal sending, which came, after the Cuban Missile Crisis, replete with hotlines. With Iran there is neither the history nor the direct communication to assure that controlled escalation remains, well, controlled.

In interviews, American intelligence officials say they continue to assess that Iran is not interested in a wider war, even as it has encouraged Houthi operations in the Red Sea. The whole purpose of the Iranian proxies, they argue, is to find a way to punch at Israel and the United States without setting off the kind of war Tehran wants to avoid.

There is no direct evidence, they say, that senior Iranian leaders — either the commander of the elite Quds Force or the supreme leader, Ayatollah Ali Khamenei — ordered the recent Houthi attacks on ships in the Red Sea. But there is no question Iran has supported the Houthi actions, and the intelligence assessments contend that Iranian officials believe the escalating conflict will increase costs to the West — without risking a wider war, U.S. officials said.

The White House has declassified information that it says shows that Iran is supplying the Houthis with weaponry, though increasingly the Houthis appear able to make many of their own, including drones assembled from parts obtained from China and other suppliers. U.S. officials believe Iranian ships and aircraft are supplying targeting data. But American spy agencies believe that the Houthis are an independent organization and that Iran is not dictating their day-to-day operations, U.S. officials said Friday.

“The question kind of at the heart of all of this is: To what extent are the actions of these proxies directed from Iran and to what extent are they local initiatives?” said Mr. Crocker, a storied former American diplomat who was posted in nations including Lebanon, Iraq, Afghanistan and Pakistan.

Mr. Crocker believes that Ayatollah Khamenei is even more effective than his predecessor was, or the Shah of Iran’s regime, in projecting power through the region. But he said he was still wrestling with the question of how much Tehran directly controls.

“I still don’t have a good answer,” he said in an interview. “One would expect that command and control is greater with Hezbollah than it is or was with Hamas,” but he said he assumed that all of the proxies “at a strategic level are guided at least by Tehran.”

What the Iranian leadership cares about the most, he argued, is “regime stability,’’ since the supreme leader is 84 and ailing.

When President Donald J. Trump ordered the killing of Maj. Gen. Qassim Suleimani, the leader of the Quds Force, in 2020, “Iran’s response to the assassination of its national hero was very measured,” noted Adnan Tabatabai, an expert on Middle East politics who focuses on Iran-Saudi relations.

What followed, Mr. Tabatabai said, was “what I would refer to as a severe deterrence crisis for Iran, because in the following two years in particular, Israel carried out the most humiliating operations on Iranian soil.” They included sabotage around the Natanz nuclear enrichment site and the remote-control assassination of the scientist at the heart of the nuclear program.

But in the four years since, Iran has deepened and sharply improved its proxy forces, supplying them with new generations of weapons, the capability to assemble their own arms and more training.

Of all the proxy forces, it may be the Houthis who feel more freedom of action from Iran’s oversight. They do not have deep roots with Tehran, the way Hezbollah does. And they have proven that they have an outsize ability to disrupt global commerce. Already the Houthis have caused Tesla and Volvo to run short of parts temporarily, and they are driving up energy prices.

While American and British forces destroyed about 30 sites in Yemen used by the Houthis, Pentagon officials said Friday that the group retained about three-quarters of its ability to fire missiles and drones at ships transiting the Red Sea. It is unclear whether it will now be deterred — or if it believes it has a duty to retaliate.

“Bombing the Yemeni resistance will not loosen any knots in the American strategy, just as it did not loosen a knot in Vietnam and Afghanistan,” Mohammad Imani, a conservative analyst, wrote in a column for Fars News, a semi-official Iranian news agency, calling the strikes “a joke.”

The Iranians continue to talk up the Houthis. On Sunday, Ebrahim Raisi, Iran’s president, praised them in a speech as “brave, powerful and fearless” for defending “the oppressed people of Palestine.” And he used the strike to try to encourage other countries to support the Palestinians, without making any commitment himself, declaring, “If the people of Islamic countries get a chance, you will see armies ready to be sent to Palestine.”

Diplomats in the Middle East say they are concerned that Israel’s hard-line government is far less invested in containing the conflict than the Biden administration is. Some theorize that they might see value in striking Iran’s proxies and drawing the United States in more directly.

.

“Iran has tried to take the conflict abroad,” said Sanam Vakil, an Iran expert at Chatham House, a London-based research organization. “Iran’s red lines are Iran’s borders. At this point, it’s very much willing to gamble around the region, but not at home.”

Yet the strategy carries risk for Iran. Mr. Biden’s options for calibrating the U.S. response would become far more limited if American soldiers or contractors died in a proxy attack — something that very nearly happened in several recent incidents. If Americans are killed, the pressure to direct attacks at Iran will rise sharply, officials acknowledge.

“For the Iranians, it’s been very good for them so far, but it’s getting to a point where it’s becoming very risky,” said Rainam al-Hamdani, a Yemen analyst who has studied the Iran-Houthi relationship. He added, “One misstep from one of these proxies, if it hits in the wrong place at the wrong time, we really risk a regional war.”

Leily Nikounazar contributed reporting.