They played various roles in a group established in Taiwan in November that later called for the overthrow of the Chinese Communist Party, Li said.
"They said they would seek international support and provide military training to Hongkongers abroad," Li told reporters.
A Facebook page matching the Chinese name of the group identified by police had fewer than 70 followers.
Police also displayed flags seized during Wednesday's operation, including one of Tibet and one bearing a slogan outlawed by Hong Kong authorities.
The four people remained in custody on Thursday.
Hong Kong enacted a separate national security law of its own last year, which officials said was needed to restore order.
As of Jul 1, authorities had arrested 333 people for various national security crimes, with 165 of them convicted.
Beijing's top official overseeing Hong Kong, Xia Baolong, said last month the city must remain on guard for national security threats and "soft resistance".
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