It later appeared before the White House press corps in the Rose Garden along with Trump, the First Lady Melania and Vice President Mike Pence. But we would like to invite readers who can afford to do so, and for whom The Times of Israel has become important, to help support our journalism by joining The Times of Israel Community.
Trump didn't touch Conan in view of reporters.
The Belgian Malinois breed, Trump said, is the "ultimate fighter, ultimate everything", and besides being able to take a person down can also sniff out drugs.
Conan was slightly injured in the operation but has since recovered and returned to active duty.
"This is a special time for Conan", he said, adding that "Conan is a tough cookie".
The medal ceremony came after Trump was criticised for sharing a fake image of the dog receiving a medal of honour after the raid.
Trump bestowed a medal on Conan and presented the dog with a plaque.
Trump used a slew of adjectives to describe Conan, which was injured when it was exposed to electric wires in the late October raid while chasing al-Baghdadi at the terrorist's compound in northwest Syria.
According to a White House official, Conan was not accompanied by his normal handler for this appearance since the handler participated in the Baghdadi raid and can not appear publicly.
The dog first rocketed to fame when Trump gave it a shout-out in his address to the nation announcing the Baghdadi raid last month.
More tweets followed, with the president eventually revealing the dog's name. Trump was briefed on the tools available to the members of the Delta team before the raid, Pence said, including their military working dogs. "Actually incredible", Trump said.
"Conan was very badly hurt, as you know".
"Conan is really a hero", Pence said, patting the dog on the head.
Trump has repeatedly praised himself for al-Baghdadi's death, working a mention into a campaign ad during the World Series just days after the Oct 26 raid in northern Syria.
The head of US Central Command, General Kenneth McKenzie, has said Conan was a "critical member of our forces" and mentioned his impressive record of 50 combat missions in four years of service. Trump, the first American president in a century without a dog of his own, stood with his hands at his side, as did first lady Melania Trump.