Somalia's extremist al-Shabaab group says its deadly terror attack on a Nairobi shopping mall is a punishment and a warning to Kenya to stop its troops interfering in Somalia, but the high-profile assault serves a much larger, much darker purpose.

Ever since the power struggle earlier this year within al-Shabaab, the group has become dominated by extreme jihadists. Long-time leader Sheik Hassan Dahir Aweys was forced to surrender to the Somali authorities after it became apparent he was outgunned within his own movement by young fighters professing loyalty to a more radical course of action. No longer content to fight in the Somali countryside, these young men were bent on taking back the Somali capital, Mogadishu, lost in 2011 when African Union troops took control, and establishing their Islamic state.

At the same time, rival leader Ahmed Abdi Godane consolidated his hold over the impressionable group, having sworn obedience to al-Qaeda chief Ayman al-Zawahiri. Unlike Mr. Aweys, who emphasized the Somali character of his organization and the national nature of his goals, the Afghan-trained Mr. Godane is comfortable with taking support, and orders, from outside.

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To the new al-Shabaab leadership, this Nairobi attack "is much more than a local battle," says Alastair Crooke, author of Resistance: The Essence of the Islamist Revolution. "It's part of a region-wide movement, a much larger sectarian conflict."

Just as the twin 1998 al-Qaeda attacks on the U.S. embassies in Nairobi and Dar es Salaam signalled the rise of Osama bin Laden, this weekend's attack in the Kenyan capital may presage a new al-Qaeda trend with a renewed emphasis on things Western.

With al-Qaeda facing setbacks in Afghanistan, Pakistan and, most recently, in Syria, where the West has made clear its comfort with keeping Bashar al-Assad in power, leaders of the organization and their benefactors in the Gulf states are ramping up their radicalism. They want to see it applied in other parts of the Islamic region, said Mr. Crooke – in Yemen, Iraq, the Maghreb, Nigeria. Most recently there has been a push in Egypt's lawless Sinai Peninsula, with attacks by a group called Ansar al-Maqdis, believed to be led by Mohammed al-Zawahiri, brother of the al-Qaeda leader, and now a campaign in Somalia.

"You're seeing this push wherever radical Sunni Islam faces those they see as apostates, be they Shia, Alawi, Sufi or what have you," said Mr. Crooke. Indeed, an attack by Sunni extremists on a church in Peshawar, Pakistan, also this past weekend, killed 78 Christians.

This region-wide effort is believed by observers such as Mr. Crooke to be part of a larger plan by certain elements in the Gulf who seek to regain lost influence.

They know that "the most successful military groups are those affiliated with al-Qaeda," he noted. "And money that used to go to Afghanistan and Pakistan now is going to groups like al-Shabaab."

Kenya's President has vowed bloody recrimination for the Nairobi attack, but this is the last thing Kenya or the African Union should do, Mr. Crooke said. "It will only inspire people to support al-Shabaab and mobilize their fighters," he said.

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"Much better, they should use their intelligence and carry out precision assaults on the leadership," said Mr. Crooke, himself a former MI5 operative in Afghanistan.