Police in Hong Kong have arrested four members of a student-led pro-independence group for suspected secessionist offenses on social media under the city's sweeping new national security law.

The arrests which included three males and one female, aged between 16 and 21 is the first since the law was imposed on the city by China on July 1, which also criminalized subversion, terrorism, and collusion with foreign forces.

In a press conference, police spokesman LEE KWAI-WAH said the organization had "posted about the establishment of a new party that advocates Hong Kong independence on social media."

Police said the four were being investigated under Articles 20 and 21 of the security law, which deal with secessionist offenses of a "grave nature" which can result in sentences of at least 10 years or life imprisonment.

The Hong Kong government has defended the law as necessary to protect national security, and promised that it would only affect a tiny number of people.