Thankfully, one image showed a vase bottom, and the green mark told us a lot. A laurel wreath with an M in the center encircled by "Hand-Painted Nippon" clearly identified the vases as Nippon ...

The Japanese chose their word Nippon for the country of origin mark. Then in 1921 our government asked the word to be changed to Japan. So, your vase was made between 1900 and 1920.