A Japanese defence ministry official said the intention of the Chinese J-15 jets was "unclear", but added that there was "no need" to lock on to the Japanese planes if their intention was to locate other aircraft.
The J-15 jets, which were launched from China's Liaoning aircraft carrier, first locked its radar on Japanese jets at 16:32 local time on Saturday (07:32 GMT) and again at around 18:37.
The official added that the Japanese aircraft "did not do anything that could be considered a provocation".
"It is extremely regrettable. Japan has strongly protested to the Chinese side, and we firmly requested measures to prevent recurrence," Takaichi told reporters Sunday in Wajima, Ishikawa prefecture.
"We will respond calmly and resolutely," she said.
The Chinese navy however said Japan's claim was "completely inconsistent with the facts" and told Tokyo to "immediately stop slandering and smearing". It added that its training exercise in the area had been previously announced.
This comes two weeks after Japan scrambled aircraft when a suspected Chinese drone was detected off Yonaguni, island near Taiwan. Tokyo has said it is planning to deploy missiles from Yonaguni in a move that has angered Beijing.
A month of heightened tensions have seen China ask its citizens to avoid travelling to Japan.
China has also banned the importation of seafood from Japan and suspended the screening of popular Japanese films.