No further details on the targeted US-based dissidents were provided.
The religious organisation hit by hackers was described as one which "previously sent missionaries to China and was openly critical of the PRC government". PRC is short for the People's Republic of China.
A Hong Kong newspaper was also on the list. While it was not named, the statement said that it was "considered as being opposed to the PRC government".
Besides US agencies, hackers were said to have targeted the foreign ministries of Taiwan, India, South Korea and Indonesia.
Last October, the FBI and the Cybersecurity and Infrastructure Security Agency said hacks targeting two major US presidential campaigns were carried out by "actors affiliated with the People's Republic of China".
Earlier last year, seven Chinese nationals were charged with running a hacking operation that lasted at least 14 years and targeted foreign critics of China.
Operations linked by Western governments to China have also targeted the UK's Electoral Commission, and the UK and New Zealand parliaments.