AMID THE frosty peaks of the Hindu Kush, I imagined the echo of George W. Bush’s words, “Justice will be done!’’ rebounding through the boulders like a snow leopard on the prowl.

Nearly nine years after the terrorist attacks on Sept. 11, 2001, it is worth remembering that killing or capturing Osama bin Laden was once front and center of the US government’s anti-terrorism policy.

No doubt, grand movements, including Al Qaeda’s global jihad, require extraordinary leadership. In South Asia, where I first covered bin Laden’s getaway from US forces in 2001 at the Battle of Tora Bora, the Saudi sheikh’s aura is still larger than life — a resounding inspiration for young jihadists.

Bathed in the mystique of his successful game of hide-and-seek, bin Laden has become a man of fewer and fewer words but also one of enduring influence. His simplistic message that America wants Muslims under its boot also resonates like a siren’s call across the broader Islamic realm from Casablanca to Jakarta.

Still, it would be wrong to think this late in the game that the United States can somehow extinguish the global jihad by killing bin Laden — or putting his head on “dry ice’’ as the CIA had planned to do back at Tora Bora.

Undoubtedly, bin Laden has morphed into an important figurehead, who for many young Muslims champions their grievances simply by staying alive.

But any effort to conclude America’s long-running “war on terror’’ will have to address the motivations that inspire bin Laden’s jihad, many of them based on long-standing conspiracy theories.

Indeed, America’s conundrum — and for that matter its war — is as much about perceptions as facts. Too often the idea of Israel’s occupation in the Holy Land is conflated in the minds of young Muslims with the idea of American military “occupation’’ in South Asia and beyond.

In my travels while researching a book about the relationship between the Arab world and the United States, I discovered that Israel — or the Holy Land — is a repository of an enormous amount of rage toward both Americans and Jews.

As General Petraeus’s Central Command articulated in a detailed “Posture Statement’’ earlier this year, “The (Israeli-Palestinian) conflict foments anti-American sentiment, due to a perception of US favoritism for Israel,’’ adding that, “Meanwhile, Al Qaeda and other militant groups exploit that anger to mobilize support.’’

Al Qaeda’s tactics in this regard are over two decades old. Consider that bin Laden’s own mentor Abdullah Azzam, a Palestinian himself, first said 1988 that “every Muslim on Earth should unsheathe his sword and fight to liberate Palestine,’’ adding that, “You must fight in any place you can.’’ By no coincidence, he was speaking in a New York City mosque and referring to Afghanistan.

The desire to “liberate’’ Palestine — or at least to see the creation of a genuine Palestinian state — has become emblematic for many Muslims of a greater struggle against the United States and Israel. Al Qaeda has crafted its own recruitment campaigns on the back of this perception.

Along Pakistan’s border with Afghanistan, radical religious schools dispense this message like a mantra as young boys rock to the poetic cadences of the Koran. In some cases, Taliban fighters, fresh from the battlefield, drop into Pakistani madrassas from Afghanistan to embellish their own heroism and ridicule the American “infidels.’’

One Pakistani religious scholar near the Afghan border actually tried to convince me that Jewish Americans had helped destroy the World Trade Center so the US military could invade South Asia.

The best way to combat these false impressions is to remove the grist from Al Qaeda’s propaganda mill and impair its ability to recruit more jihadists.

That is why America should be pushing harder to end our own occupations and those of our allies. This can be accomplished by concentrating on providing the benefits of a successful counterinsurgency campaign in South Asia, but also by persuading Israel — with the use of real leverage — that ending its own occupation of the West Bank is in the long-term interest of both Israel and the United States.

A two-state peace deal for Israel and Palestine will be a boon for peace around the world and here at home. A US foreign policy that does not endeavor to accomplish these ends will not do justice to the goodwill and peaceful aspirations of America’s fighting men and women.