A supermarket chain took steps Thursday to ease the water drama faced by Tokyo families after local officials said Wednesday that infants shouldn't be given city tap water due to higher-than-normal radiation levels detected in some parts of the city's water supply, the latest consequence from the troublesome Fukushima nuclear power plant over 150 miles north.

While the news on Tokyo's water was better Thursday, with radioactive iodine levels detected falling back below permissible limits, Ito-Yokado, a grocery chain owned...