China said on Thursday the United States should respect its air defence identification zone (ADIZ), after CNN reported China had warned a U.S. bomber it was illegally flying inside China's self-declared zone in the East China Sea.

China declared the zone, in which aircraft are supposed to identify themselves to Chinese authorities, in the East China Sea in 2013, which the United States and Japan have refused to recognise.

CNN, citing the US Pacific Air Forces, said the B-1 bomber was flying near South Korea on Sunday, and that its pilots responded to Chinese air traffic controllers saying they were carrying out routine operations in international airspace, and that the aircraft did not deviate from its flight path.

Chinese Foreign Ministry spokeswoman Hua Chunying said she had not heard of the matter, and referred questions to the Defence Ministry, which did not immediately respond to requests for comment.

"But, generally speaking, I hope that in this region all countries' actions consider the security concerns of relevant countries and be beneficial for mutual trust, peace and stability between countries," Hua told a daily news briefing.

"The United States has its own ADIZs. I think if this matter is true, they should respect China's relevant ADIZ rights," she added, without elaborating.