Eliminating the Islamic State group's elusive leader gives President Donald Trump a new argument for leaving Syria, but the U.S. military campaign against the extremists is far from finished.

The killing of Abu Bakr al-Baghdadi by U.S. forces leaves the Islamic State without an obvious leader, a major setback for an organization that in March was forced by American troops and Kurdish forces out of the last portion of its self-declared "caliphate," which once spanned a swath of Iraq and Syria.

But the militant group, which arose from the remnants of al-Qaida in Iraq after that group's defeat by U.S.-led forces in 2008, has ambitions to regenerate again. And it remains a dangerous threat in Iraq, Afghanistan and beyond.

"The bottom line is: This puts the enemy on its heels, but the ideology — and this sounds so cliched — it is not dead," said Chris Costa, a former senior director for counterterrorism for the National Security Council in the Trump administration.

Key to the Islamic States is its "kill where you are" ethos, encouraging a far-flung network of followers, including those in the United States, to commit violence however and wherever they can. That jihadist message is likely to live on, even with the death of al-Baghdadi.

Read more: ABC News