I think I've seen the same argument in reverse somewhere in the forum: Japanese residence tax doesn't qualify for the US Foreign Tax Credit. The basic reasoning seems to be that a residence tax doesn't technically qualify as an income tax. Also, in the case of the IRS, the stated position is "You can claim a credit only for foreign taxes that are imposed on you by a foreign country or U.S. possession." So one might say that because residence tax is imposed by the municipality rather than the country, it doesn't apply.
The trouble is, first, that except for a flat fee of a few thousand yen, residence tax IS based on income even though it doesn't call itself an "income tax." Second, the IRS explicitly defines "foreign country" as follows (same web page): "A foreign country includes any foreign state and its political subdivisions. Income, war profits, and excess profits taxes paid or accrued to a foreign city or province qualify for the foreign tax credit."
It's hard to interpret this definition as not applying to Japanese prefectures and municipalities, which are obviously political subdivisions of the state. As a result, I believe that (many? most?) expat accountants routinely include residence tax in the FTC, although because of the way residence tax is collected, they have to work with accrued rather than paid taxes. They may be wrong, of course, but still...
By the same logic, U.S. state (and city) taxes would seem to qualify for the Japanese version of the foreign tax credit. On the other hand, I've never had to substantiate that position officially, so YMMV, although TokyoWart's experience is suggestive.