WASHINGTON (Reuters) - Deadly attacks in four countries linked to Islamic State show the limitations of U.S.-led efforts to loosen the group’s grip in Syria and Iraq, and the challenge of stopping attacks that are not only globally dispersed but very different in their choice of targets, current and former U.S. officials said.

Firemen inspect the site of a suicide car bomb in the Karrada shopping area, in Baghdad, Iraq July 3, 2016. REUTERS/Khalid al Mousily

“Bombing the heck out of (Islamic State’s capital) Raqqa is not going to stop this stuff,” said Paul Pillar, a veteran CIA analyst now at Georgetown University.

In recent months, Obama administration officials have frequently portrayed the group’s deadly strikes worldwide as a direct response to the U.S.-led military coalition’s success in ousting it from large tracts of Iraq and Syria.

While that may be true in part, the current and former U.S. officials said, it is overly simplistic and understates how Islamic State’s influence has spread beyond the territory it controls.

The ultra-hardline Sunni Muslim group’s recruiting and propaganda directed outside its self-proclaimed caliphate long predates its loss of key cities in Iraq such as, most recently, Falluja, U.S. officials said.

“Evidence has been growing for some time that ISIS has been expanding its outreach, recruiting and propaganda, both online and with emissaries, as the military and economic costs of maintaining, much less expanding, its original caliphate have become clear,” said a U.S. official who closely watches militant Islamic groups.

In its new guise, some analysts said, Islamic State is coming to more closely resemble al Qaeda, which has primarily focused on large-scale attacks rather than try to hold territory.

Building and maintaining a caliphate has possibly been more expensive and complicated than Islamic State first realized, the U.S. official said.

U.S. officials said they are still analyzing the links between Islamic State and a June 28 attack on Istanbul airport that killed 45 people; an attack on a cafe frequented by foreigners in Dhaka on Friday that killed 20 people; a suicide truck bombing in a mainly Shi’ite Baghdad neighborhood on Saturday that killed at least 175 people; and attacks in Saudi Arabia targeting U.S. diplomats, Shi’ite worshippers and a security office at a mosque in the holy city of Medina.

All took place during the Muslim holy month of Ramadan, which ends this week with the Eid al-Fitr feast.

A U.S. official said the attacks in Turkey, Iraq and Saudi Arabia appear to have direct links to Islamic State. The one in Bangladesh may have been Islamic State-inspired but also have local roots, the official said.

Intercepted Islamic State messages suggest targets to attack, including gathering places for non-Muslims and Shi’ite Muslims in predominantly Sunni areas, and government installations, another U.S. official said.

“There’s a fair amount that falls somewhere in between inspiration and outright direction,” this official said. “Call it suggestion.”

Counter-terrorism experts say there is no silver bullet that will stop strikes on civilians that are so globally dispersed and use methods of attack that range from single suicide bombers to massive truck bombs to hostage-taking.

“The challenge involved is, the action and initiative is coming from a lot of different places,” said Georgetown’s Pillar.

Closer diplomatic cooperation, intelligence sharing and tracking money flows were crucial, he said.

“We’ve always made clear that the military campaign is not enough to defeat Daesh (Islamic State) or to remove the threat that it poses,” State Department spokesman John Kirby said on Tuesday. “A holistic campaign that addresses the root causes of extremism is the only way to deliver a sustainable defeat.