In a press conference late Wednesday, 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."

"We have to enforce the laws even if the crimes are committed on the internet. Don't think you can escape from the responsibility in cyberspace and commit crimes," Lee added.

Police said the four were being investigated under Articles 20 and 21 of the security law, which deal with secession. Under the law, secessionist offenses of a "grave nature" can result in sentences of at least 10 years and up to life imprisonment, while lesser offenses carry penalties of between three and 10 years.

On Sunday, the group published a post titled "counter Chinese nationalism, build Hong Kong nationalism," which linked to the Facebook page and recruitment forms for the "Hong Kong Studentlocalism US Division." The group's US page says it is "committed to push forward Hong Kong nationals' path of regaining our right of self-determination, and push forward Hong Kong's path towards independence."

Soon after the arrests, a CNN reporter had a source cancel an interview, unrelated to the security law, "in view of the latest development in Hong Kong."

In a statement, Sophie Richardson, China director for Human Rights Watch, said the arrests were a "gross misuse of this draconian law (which make) clear that the aim is to silence dissent, not protect national security."

She added that they "raise chilling concerns of a broader crackdown on political parties" as September's legislative elections approach.

However, the chance of those elections going ahead as planned has been thrown into doubt this week, amid reports the government may exercise emergency powers to delay them to 2021, due to a recent rise in coronavirus cases in Hong Kong.

The nomination period for the election ends on Friday, with polls due to open on September 6.

The city has recorded over 100 new coronavirus infections every day in the past week, up from zero cases in late June. Wednesday marked the first day of the strictest social distancing measures Hong Kong has seen so far: masks mandated in indoor and outdoor public spaces, no more than two people per group when gathering in public, and no in-restaurant dining.

Ronny Tong, a member of Hong Kong's Executive Council or de facto cabinet, told CNN he does not know how long any delay might be, but that any decision to delay the elections would be due to public safety concerns.

"I hope people will understand that any delay is due to community safety and not political considerations. Hong Kong people still have a right to vote freely," Tong said.

The city's Registration and Electoral Office said it was "closely monitoring" the coronavirus outbreak in the city and its potential impacts the election and would "listen to advice from the Government and health experts."

Pro-democracy figures have denounced any suggestion of postponing the election. Activist Joshua Wong said the pandemic was an excuse, adding that the government was "afraid they will receive landslide loss in the upcoming election."

Opposition parties were aiming to ride a wave of discontent with the government to an historic victory in the semi-democratic legislature, where just under half the seats are controlled by so called functional constituencies, which represent business and society groups and are typically pro government.

Last year, pro-democracy candidates won a landslide victory in local council elections. A similar result in the legislative council could put them in a position to force a constitutional crisis by blocking the budget and pressuring Lam to resign. Both the Chinese and Hong Kong governments have suggested such a plan could be illegal under the new national security law.