A US military dog who played a starring role in the raid that killed Islamic State leader Abu Bakr al-Baghdadi has been honoured at the White House – although he appeared oblivious to the praise President Donald Trump heaped on him.

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

Mr Trump used a slew of adjectives to describe “ultimate fighter” Conan, who was injured when he was exposed to electrical wires in the late October raid while chasing al-Baghdadi at the terrorist’s compound in north-west Syria.

The special forces dog is believed to have been sent down a tunnel after al-Baghdadi because US troops suspected he was wearing a suicide vest. Al-Baghdadi detonated the vest in the tunnel, killing himself and three children.

The President called Conan “incredible, brilliant, smart and very special” at Monday’s White House appearance.

“This is Conan,” Mr Trump said. “Right now, probably the world’s most famous dog.”

He bestowed a medal on Conan and presented the “tough cookie” with a plaque. First lady Melania Trump stood nearby.

The President said initially Conan was going to be muzzled for his White House appearance but Mr Trump said he thought that would put the dog in attack mode.

“He’s not in a bad mood today,” he told dozens of reporters, cameramen and members of TV crews gathered in the Rose Garden on Monday. “You’re safe.”

Although, he did warn that Conan would turn on reporters who asked questions.

“It’s trained that if you open your mouths, you will be attacked. You want to be very, very careful,” he said.

Conan is a very good boy! We were proud to honor him at the White House for his terrorist-hunting skills. 🇺🇸 pic.twitter.com/UL56lGihuG

— The White House (@WhiteHouse) November 25, 2019

Mr Trump said he asked members of the US special forces who met him on Monday (local time) if an unarmed man would stand a chance against Conan. The fighters, who could not appear in public, told him “No”.

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

-with AAP