A US military dog that played a starring role in the raid that killed the Islamic State group's leader, Abu Bakr al-Baghdadi, seemed oblivious to the praise President Donald Trump heaped on him at the White House on Monday.

Key points: The explosion Baghdadi set off during the raid injured the dog

The explosion Baghdadi set off during the raid injured the dog Mr Trump said he bestowed a medal on Conan and presented the dog with a plaque

Mr Trump said he bestowed a medal on Conan and presented the dog with a plaque "Conan is really a hero," Vice-President Mike Pence said

Conan, a Belgian Malinois, seemed much more interested in the head scratches he was getting from Mike Pence, repeatedly looking up at the Vice-President in search of more attention.

Mr Trump used a slew of adjectives to describe Conan, injured while chasing Baghdadi at the terrorist's compound in northwest Syria in late October.

He called the dog "incredible", "brilliant", "smart", the "ultimate fighter", "very special", and a "tough cookie".

"So this is Conan," Mr Trump said. "Right now, probably the world's most famous dog."

Mr Trump said he bestowed a medal on Conan and presented the dog with a plaque.

Conan received plenty of head scratches from Mr Pence. ( AP: Evan Vucci )

First lady Melania Trump stood a few feet away.

The President initially said Conan was going to be muzzled for the appearance, but then said he thought that would put the dog in attack mode.

"He's not in a bad mood today," Mr Trump told dozens of media crews gathered in the Rose Garden. "So you're safe."

Mr Trump said he asked members of the US special forces who met with him on Monday whether an unarmed man would stand a chance against Conan.

He said the special forces officers, who cannot appear in public, replied: "No."

"Conan is really a hero," Mr Pence said, patting the dog on the head.

After the October raid, Mr Trump praised Conan on Twitter, calling him a "wonderful dog".

US Army General Mark Milley told a Pentagon news briefing after the raid that Conan "performed a tremendous service" in tracking down Baghdadi in a tunnel beneath his compound.

Baghdadi was killed by an explosion he himself set off, killing two children in the process and wounding Conan.

AP/ABC