The idea was simple: When a big war with Israel broke out, all the members of the Iranian-backed network of militias in the Middle East known as the “axis of resistance” would join the fight in a coordinated push toward their shared goal of destroying the Jewish state.

Iran came up with the strategy and invested tremendous resources to build each group’s fighting abilities and connect them to one another.

But the axis’s response as Israel has pummeled Hezbollah in Lebanon in recent weeks — killing many of its commanders and assassinating its leader — has so far been feeble, suggesting that the axis is weaker and more fragmented than many in the region had expected and that Iran feared that widening the war could cause Israel to turn its firepower on Tehran.

“The so-called axis of resistance from its very beginning was more or less a propaganda fiction created to enhance the prestige of the Islamic Republic,” said Ali Alfoneh, a senior fellow at the Arab Gulf States Institute in Washington.

In recent years, Mr. Alfoneh said, the network’s members had chalked up some small military victories, “but when it comes to more serious adversaries, or a state actor like Israel, it is a different game.”

Iran cobbled together the axis out of armed groups that shared antipathy toward Israel and the United States but until then had been fighting more local battles. The United States classifies most of them as terrorist organizations.