ERBIL, Iraq — Meeting with the American ambassador some years ago in Baghdad, Prime Minister Nuri Kamal al-Maliki detailed what he believed was the latest threat of a coup orchestrated by former officers of Saddam Hussein’s Baath Party.

“Don’t waste your time on this coup by the Baathists,” the ambassador, Zalmay Khalilzad, chided him, dismissing his conspiracy theories as fantasy.

Now, though, with Iraq facing its gravest crisis in years, as Sunni insurgents have swept through northern and central Iraq, Mr. Maliki’s claims about Baathist plots have been at least partly vindicated. While fighters for the extremist Islamic State in Iraq and Syria, once an offshoot of Al Qaeda, have taken on the most prominent role in the new insurgency, they have done so in alliance with a deeply rooted network of former loyalists to Saddam Hussein.

Image Izzat Ibrahim al-Douri Credit... Karim Sahib/Agence France-Presse — Getty Images

The involvement of the Baathists helps explain why just a few thousand Islamic State in Iraq and Syria fighters, many of them fresh off the battlefields of Syria, have been able to capture so much territory so quickly. It sheds light on the complexity of the forces aligned against Baghdad in the conflict — not just the foreign-influenced group known as ISIS, but many homegrown groups, too. And with the Baathists’ deep social and cultural ties to many areas now under insurgent control, it stands as a warning of how hard it might be for the government to regain territory and restore order.