The trademark application for the tablet was turned down because the name was "merely descriptive" and did not create a unique meaning, it said.
But Apple still has until July to persuade the Patent Office that the smaller tablet differs sufficiently from its iconic sibling.
Apple has been involved in a series of patent disputes with rival firms.
It won a landmark case against Korea's Samsung last year but this month, a judge in the US ordered the $1bn (£660m) in damages awarded to Apple be cut by 40% and set a new trial to assess the level of damages.
The award was the biggest in a series of global legal fights between the two companies over patents.
The Patent Office issued the letter in January, although it has only just emerged.