Osamu Fujimura told reporters in Tokyo that “this was an issue between the governments”.
It comes as China expressed regret over protesters attacking the US ambassador’s car in Beijing on Tuesday.
Chinese dissident and artist Ai Weiwei filmed the attack, a copy of which was uploaded on YouTube.
Tensions have been high between Japan and China after Japan purchased three of the disputed islands, known as Senkaku in Japan and Diaoyu in China, from a private owner.
Both Japan and China, as well as Taiwan, claim the uninhabited but resource-rich islands that are controlled by Japan.
Over the last week anti-Japanese protests in China have forced Japanese businesses to close or scale down operations.
In some cities on Tuesday, Japanese shops were attacked and vandalized on the anniversary of an incident in 1931 which led to Japan’s invasion of north-east China. The protests appeared to have diminished on Wednesday.
“Regarding damage to our embassies and consulates, we plan to demand compensation [from China] as it is an issue between the governments,” Osamu Fujimura is quoted as saying in Tokyo.
He added that any damage to Japanese property in China should be handled under local laws.
Osamu Fujimura also said that the Japanese prime minister is planning to send a special envoy to China as part of efforts “to resolve the issue cool-headedly through various diplomatic routes”.
When asked whether China would pay for damages related to the protests, Chinese Foreign Ministry spokesman Hong Lei said that relevant cases would be handled appropriately, state-run news agency Xinhua reports.
Meanwhile, China has expressed regret over the incident involving protesters that attacked US Ambassador Gary Locke’s car in Beijing on Tuesday, the US State Department said.
Its spokeswoman, Victoria Nuland, said that the US had registered its concern with China over the incident in Washington and Beijing.
Protesters chanted anti-American slogans and said that the disputed islands were part of Chinese territory as they tried to prevent the car from entering the embassy.
Ai Weiwei said he was able to shoot video footage of the attack from a friend’s place nearby.
Hong Lei said that the incident was an “individual case”, and that they were investigating it.
The US, which is an ally of Japan, has said that it would remain neutral on the islands dispute.
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