“Our ‘K-9,’ as they call it,” Mr. Trump said, “I call it a dog. A beautiful dog — a talented dog — was injured and brought back.”

The soldiers who helped capture Mr. al-Baghdadi will no doubt be the subject of intense public interest going forward — and, if history holds, so will the dogs they used as their first line of defense. After the raid that killed Osama bin Laden in 2011, the identity of the dog who aided a team of Navy SEALs when they pushed into the terrorist leader’s compound, a Belgian Malinois named Cairo, became the subject of rampant curiosity.

On Sunday, neither the White House nor the Pentagon would respond to requests for details about the animals used in the pursuit of Mr. al-Baghdadi . But Ron Aiello , a retired Marine and president of the nonprofit U.S. War Dogs Association , said in an interview that the dogs were probably one of two breeds: A German shepherd or a Belgian Malinois , two of the most common breeds deployed during similar military operations because of their strength and ability to sniff out explosives.

“If they’re leading the patrol,” Mr. Aiello said, “they want a dog that is not only an explosive detection dog but on command can be aggressive. On a mission like this you want a dog that can be aggressive when necessary.”

As the nature of terrorist attacks have changed in recent years to target airports, malls and other public places, bomb-sniffing breeds — a list that also includes Labrador retrievers — have become a sought-after law enforcement and military tool. Prices can exceed $25,000 per dog, and experts have long warned of a shortage. When they are used for military purposes, dogs like Cairo are often outfitted in their own protective gear, including waterproof vests with night-vision cameras that can be used by handlers to see what their dogs see.