Israel’s bombing of an Iranian Embassy building in Damascus, which killed senior Iranian military and intelligence officials, is a major escalation of what has long been a simmering undeclared war between Israel and Iran.

But while the strike is a vivid demonstration of the regional nature of the war, Iran has been careful since Hamas attacked Israel on Oct. 7 to avoid a larger conflict that could threaten its own government, which is already under significant internal strain.

Iran promises major retaliation, but neither Israel nor Iran wants a major shooting war, given the stakes for both countries. Even so, the danger of a miscalculation is ever-present, as both countries press for advantage in Gaza and southern Lebanon.

The Iranian officials who were killed had been deeply engaged in arming and guiding proxy forces in Gaza, Lebanon, Syria, Iraq and Yemen as part of Iran’s clearly stated effort to destabilize and even destroy the Jewish state.

For Israel’s prime minister, Benjamin Netanyahu, who presumably approved such a sensitive attack, the successful elimination of such key Iranian military figures is a political coup. It comes at a time when demonstrations calling for his resignation have increased in intensity, as the war against Hamas drags on and Israeli hostages remain in Gaza.

Displaying its ability to infiltrate Iranian intelligence, Israel is trying to hit the operational part of Iran’s regional proxies, its so-called Axis of Resistance to Israel, aiming to weaken and deter them, even as the war in Gaza continues.

Mr. Netanyahu has emphasized for years that Israel’s main enemy is Iran and its nuclear program, and this strike may help him “rehabilitate his reputation as ‘Mr. Security,’” said Sanam Vakil, director of the Middle East and North Africa program at Chatham House.

But that will be difficult to pull off, she said, with Israel bogged down in Gaza, Hamas so far unbeaten and Iran and its proxies undiminished. For the same reasons, Mr. Netanyahu and the Israeli military want to weaken and deter Iran’s proxies, but without sparking a full-scale war with Hezbollah, the Iran-backed group that controls southern Lebanon and has been trading sporadic fire with Israel across the border.

Iran has vowed retaliation and revenge for what it called an unprecedented attack, but it is also in a bind, analysts argue.

U.S. officials do not believe that Iran initiated the Hamas attack or was even informed about it in advance, and since Oct. 7 “Iran has been clear that it does not want a regional war,” Ms. Vakil said. “It sees this conflict with Israel playing out over a longer time frame.”

“But this strike will be difficult for Iran to ignore,” she added, “because it is a direct attack on its territory” and killed three senior commanders of Iran’s Quds Force, the external military and intelligence service of the Islamic Revolutionary Guards Corps.

Iran said the Israeli strike killed an Iranian general, Mohammad Reza Zahedi, along with his deputy, a third general and at least four other people, reportedly including senior officials of Palestinian Islamic Jihad, an Iranian affiliate that is also fighting in Gaza.

The killing of General Zahedi, who was said to be in charge of Iran’s military relationship with Syria and Lebanon, is widely considered the most important assassination of an Iranian leader in years.