TOKYO—As it works its way back toward a five-and-a-half year high reached in May, Japan's stock market faces a new headwind as the government moves forward with a planned doubling of tax rates on capital gains and dividends.

Government officials and brokerages are betting that a new program will offset any negative impact from the higher rates, as well as aiding the economy by encouraging more people to invest in shares. The initiative—heavily marketed with images of cuddly dogs and the endorsement of baseball star Ichiro...