Shimomura said Abe was particularly concerned by Yanagisawa's remark which he described as "inappropriate".
Kyuma, one of the more liberal members of Abe's cabinet, started the ball rolling when he described the US invasion of Iraq as a "mistake", "based on an assumption that weapons of mass destruction existed".
Hakuo Yanagisawa, the health minister, called
women "birth-giving machines" [Reuters]
The defence minister made the comments hours after George Bush, the US president, delivered his annual state of the union address on January 23.
Under intense pressure, Kyuma later said his remarks were misinterpreted and that he had meant to say that he thought at the time of invasion that the US needed to be "more cautious".
Japan, the staunchest American ally in Asia, had sent several hundred troops to Iraq on a humanitarian mission to support the US-led invasion.
Yanagisawa's remarks on Saturday came during a speech on Japan's falling birthrate, and drew criticism from the opposition and the ruling bloc.
"The number of women between the ages of 15 and 50 is fixed. The number of birth-giving machines [and] devices is fixed, so all we can ask is that they do their best per head," Yanagisawa reportedly said.
The minister later apologised and retracted his remarks. "You can't just say whatever you please in this cabinet," Yasuhisa Shiozaki, the administration's top spokesman, said.
The public gaffes come as Abe's support ratings have hit their lowest level and opinion polls show weakening support for his cabinet.
Abe's administration faces crucial parliamentary elections in July.