Citing unnamed sources, Kyodo news agency said on Friday that Koizumi had abandoned a controversial proposal that could have paved the way for a female to take the throne in Japan.
The imperial household said on Tuesday that Kiko, the 39-year-old wife of the emperor's second son, is pregnant, a dream come true for opponents of female succession to the Chrysanthemum Throne.
If she has a baby boy, it would be the first male born into the royal family since her own husband, Prince Akishino, in 1965.
She is reportedly due in late September, just when Koizumi is set to retire.
Koizumi has pledged to revise imperial law by June, but conservatives had stepped up a campaign against maternal succession in recent weeks.
The succession issue has come to the fore as Crown Prince Naruhito and Crown Princess Masako have had only one child, four-year-old Princess Aiko, in nearly 13 years of marriage.
Masako, 42, a US-educated former career woman, is under intense pressure to bear a son and makes few public appearances due to stress.
Koizumi is planning to retire in
September this year
Conservatives have made no secret they hoped Kiko, a housewife, would have another child, after having two daughters.
They have also suggested that female-line succession could be avoided by choosing a future husband for Aiko or restoring royal status to families that lost their titles after World War II under US occupation authorities.
Opinion polls show overwhelming support for letting Aiko sit on the throne, which would make her Japan's first reigning empress since 1771.