Nine days after the September 11, 2001, attacks, President George W. Bush stood before Congress to outline a two-pronged response to history's deadliest terrorist act: dramatic improvements in security at home and an all-out assault against what he called a "fringe form of Islamic extremism" at war with the West.

Fifteen years later, the first goal arguably has been met, as Americans by almost every measure are safer today from another 9/11-scale attack than in 2001.

Yet the struggle to defeat the global network of violent, rabidly anti-Western jihadist groups has recorded fewer successes. Indeed, the problem appears to have grown bigger.

The al-Qaeda organisation once led by Osama bin Laden has been decimated and is no longer capable of orchestrating a sophisticated, transnational plot on its own, terrorism experts say they believe. Al-Qaeda's branches in North Africa and Yemen also have been weakened by Western military strikes and ongoing fighting with rival factions.

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But al-Qaeda's powerful and locally popular Syrian branch, Jabhat Fateh al-Sham, commands an army of thousands of trained fighters and now serves as a base for senior al-Qaeda operatives experienced in making explosives and carrying out terrorist attacks. The Syrian group recently announced it had split with al-Qaeda, but US officials say the claim is not credible.

Isis (Islamic State), despite military setbacks in Iraq and Syria, has demonstrated a growing capability to direct - or inspire - simple-but-lethal terrorist attacks around the world.

"The threat is actually worse: It has metastasised and spread geographically," said Richard Clarke, a top terrorism adviser to three presidents and the man who famously warned the Bush Administration about the growing risk from al-Qaeda in the weeks before 9/11. "Today there are probably 100,000 people in the various terrorist groups around the world, and that's much larger than anything we had 15 years ago."

Both the Bush and Obama administrations thwarted multiple terrorist plots and achieved significant military successes against specific terrorist factions and key leaders, including al-Qaeda in Iraq founder Abu Musab al-Zarqawi in 2006, bin Laden in 2011 and Isis' No. 2 commander, Abu Muhammad al-Adnani, who reportedly was killed in a US airstrike last month. Yet both administrations struggled to find a formula for blunting the appeal of violent jihadist groups or preventing thousands of young Muslims from enlisting in a global movement.

There is little to show for more than a decade's worth of US-sponsored programmes aimed at countering extremist messages, terrorism experts say, and US officials have struggled to block the jihadists' use of social media or disrupt international funding and support for extreme interpretations of Islam. US policies, from the Iraq invasion in 2003 to the ongoing use of armed drones against suspected terrorists, have helped drive new recruits to al-Qaeda and Isis.

"We generate more enemies than we are able to take out," said former Congresswoman Jane Harman a chairwoman of the House Intelligence Committee in the years after 9/11, who now is president of the Woodrow Wilson International Centre for Scholars. "Our military power remains extraordinary. But winning this fight requires projecting a narrative about American values and interests. And we have failed to do that."