According to what I can make out in he phot,o around the top it says 大big 日本Japan. In the middle is the character 夕 xi1. In chinese that character means dusk or sunset. It may have a similar meaning in Japanese. Good luck.
Thank you very much Yang Huo for this interesting comment. I will look in this direction. Actually the setting sun symbol is written "夕日" in Japanese. The setting sun is Japan's most common national symbol, used since first Chinese-Japanese war(1894-95) to Pacific War (1941-1945). It complements well with "Great Japan" inscription. This all fits to style of this vase - late Satsuma style.