Twice this week, presidential spokesman Manuel Adorni was asked about Milei's English Mastiff, Conan, said to have died seven years ago.
Milei, 53, had Conan cloned, and today is believed to own four copies he refers to as "four-legged children."
Or is it five?
The president himself referred in an interview with CNN this month to his five dogs, whose faces and names he had engraved on the presidential baton.
Conan, Milton, Murray, Robert and Lucas were also among the first Milei thanked after his election victory last August.
Yet, only four mastiffs -- enormous animals that can weigh up to 100 kilograms (220 pounds) -- have ever been seen in photos with Milei.
At a press conference Thursday, Adorni was asked if Milei has four dogs -- but sees five -- and if so, whether he can be said to have a firm grip on reality.
Adorni shot back that it is "disrespectful to describe the president as a person who speaks to things that do not exist. It seems to me to be absolutely disrespectful... it is to mess with his family."
The spokesman did not clarify how many dogs the president owns.
On Monday, Adorni answered a similar question by stating: "I don't see what the difference is whether it be four or five dogs or 43 rabbits."
'The Madman'
Often described as eccentric, Milei raised eyebrows on the campaign trail by occasionally dressing up as a superhero alter-ego "Captain Ancap" -- short for anarcho-capitalist.
He also repeatedly wielded a live chainsaw to illustrate the deep cuts he would make to state spending.
And then there are the dogs.
According to journalist Juan Luis Gonzalez, author of the unauthorized Milei biography "The Madman," Conan died in 2017.
The dog had been named after the muscled fictional hero Conan the Barbarian.
Devastated by the loss, Milei sent Conan's cells to US-based firm PerPETuate, which states on its website that five pups were the result of a cloning process, though only four appear on a photo that accompanies the post.
Milei has said the clones were named after economists Milton Friedman, Murray Rothbard and Robert Lucas.
Gonzalez's book also claims the wild-haired Milei consults all his dogs -- dead and alive -- with the help of a medium specialized in "interspecies communication."
The medium, Celia Melamed, recently told TN television she had helped Milei "overcome the grief over his dog."
And politician Rafael Bielsa -- who had previously worked with the now-president in the private sector -- told Argentine media Milei had spoken to him about receiving "divine" messages via Conan.
Milei himself has refused to answer questions about his dogs.
For Gonzalez, "while it may seem like a laughing matter, this is a subject concerning the mental health of the president" and its impact on government.
Milei's predecessor Alberto Fernandez entered the fray this week in a social media tiff with the incumbent, stating on X: "You must know, my dog does not advise me and is alive."
Protesters, too, have jumped at the chance to make fun, with university students proclaiming "Without science, no Conan!" at a rally against funding cuts on Tuesday.
One walked an invisible "dog" on leash at the end of an empty collar with the name "Conan" on it.
