It was the first time for the government to disclose its detection of a foreign submarine in the contiguous zone near the Senkakus.
Ministry officials say Cheng rebuffed Japan's protest, saying the islands are part of China's territory.
Japanese Vice Foreign Minister Shinsuke Sugiyama issued a protest to the Chinese embassy in Tokyo.
Beijing's foreign ministry spokesman Lu Kang said Thursday China was exercising its territorial rights in its naval deployment.
Japan lodged a formal protest with China on Thursday after detecting a Chinese frigate and an unidentified foreign submarine in waters close to the disputed Senkaku Islands in the East China Sea.
Located around 150 km northeast of Taiwan, the uninhabited Senkaku Islands have an area of about 7 sq km and are said to possibly be rich in marine and energy resources.
Chinese Frigate, Unidentified Submarine Enter Japan-Claimed Waters Near Senkaku Islands
The submarine's presence was confirmed by a Japan Maritime Self-Defense Force escort ship and a P-3C aircraft, the statement said.
The submarine was seen again on Thursday along with the Chinese frigate, and both had left the area by Thursday afternoon, according to the ministry. Indeed, with tensions showing positive signs on the Korean Peninsula between North Korea and South Korea, then China's actions near the Senkaku Islands (named Diaoyu Islands in China) is extremely shallow.
China and Japan traded accusations on Thursday after a Chinese navy vessel was detected in waters near disputed islands in the East China Sea, adding fresh uncertainty as the two sides try to improve bilateral ties. It left Thursday afternoon. The Japanese Ministry of Defense did not immediately clarify if the Chinese frigate, which was a Type 054A Jiangkai-II-class frigate, belonged to the People's Liberation Army-Navy (PLAN) or the China Coast Guard, which uses the Type 054A as well.
Japanese Prime Minister Shinzo Abe responded to the incidents Thursday by giving instructions to prepare for all possible contingencies and to coordinate closely with the USA, according to a statement released by his Cabinet. Japan's Chief Cabinet Secretary Yoshihide Suga warned China "not to undermine the trend of improvement in Japan-China relations".
Maritime confrontations and jet interceptions between China and Japan have become commonplace in recent years, especially around the Senkakus. The Chinese ship did not enter Japanese territorial waters.
Japan saw foreign submarines navigating in its contiguous zone in 2013, 2014 and 2016.