I think I remember Lizzie Collingham's book, A Taste for War, which mentions the Japanese problems with supplying their troops and feeding the general population. The commander of the Japanese in Gudalcanal (Solomon Islands) estimated about 5,000 casualties from fighting, and 15,000 from starvation and disease. However I don't have any books on the campaign in China, (and I can't find my Collingham book so I'm quoting from memory here) but the Chinese Nationalist Government did have a lot of starvation, though they also had more farming land in comparison to Islands occupied by the Japanese, so perhaps someone else will have more information. A lot of people died from starvation, disease and climate on the eastern front, and the Japanese were perhaps the least fed major military force, aside from the Russians.

This table, excerpted from the book Imperial Japan's World War Two: 1931-1945 by Werner Gruhl, seems to be what you're looking for. The numbers themselves are mainly taken from John Dower's War Without Mercy and Micheal Clodfelter's Warfare and Armed Conflicts.

Alright, I'll try and help you here:

As PromiseNotAThrowaway states, War Without Mercy states around 400-500,000 Japanese KIA in China along with a similar amount caused by US forces and another 400,000 dead in the Australian, British, and Dutch areas. Adding in the 400,000 IJN casualties (primarily due to US efforts) and you're looking at something like 1.8 million total military deaths, of which around ~25% were caused by the Chinese.

However, the question in the OP also states what % of Japanese casualties were caused by fighting the Chinese. I've seen conflicting estimates in this regard. I've seen anything from ~500,000 to more than 1 million wounded. Unlike in most of the Pacific battles, the Japanese actually had a large amount of troops that were merely wounded, as opposed to fighting to the death. For instance, the battle of Okinawa featured a death rate of something like 11 in 12 for the Japanese. One the other hand, in the Chinese campaigns, to cite the battle of Shanghai as an example, out of 90,000 casualties 20,000 were WIA or MIA. So it is very possible that while the amount of actual deaths were far higher in battles against the US, the total amount of casualties suffered is highly variable, not the least due to the political nature of the topic today-for instance, I believe the CCP has done studies on the total casualties of the war, and every year the casualties in the estimate rise.