Mr Koizumi initially pledged to put the bill to parliament by June
Mr Koizumi's slower approach came one day after the news that Princess Kiko was pregnant, raising hopes a male heir may yet be born into the royal family.
"I want to proceed cautiously so as not to make this a political tool," Mr Koizumi said of the controversial bill.
The bill was first proposed because no male royal has been born for 40 years.
But the imperial agency announced on Tuesday that Princess Kiko, the wife of Emperor Akihito's second son Prince Akishino, was pregnant.
If she has a son, it could dramatically alter the current situation in the imperial family, where there has been increasing concern over who will succeed the throne after Crown Prince Naruhito.
Naruhito, first in line to the throne after his father Akihito, has just one daughter with his wife, Crown Princess Masako.
Princess Kiko and Prince Akishino currently have two daughters.