Police said they arrested four people in Causeway Bay on Saturday on suspicion of disorder in public places and doing an act or acts with seditious intention.
Four others suspected of breaching public peace were brought to the police station for further investigation.
The police said they took action after noticing some people were displaying protest items carrying seditious words, chanting slogans and committing illegal acts in the area.
"Police are highly concerned about some people attempting to incite and provoke others to commit illegal acts that endanger national security, public order and public safety," the force said in a statement.
"Police will continue to step up patrols and enhance intelligence-gathering, closely monitor the situation of various districts and strive to prevent and combat crimes."
Officers were seen patrolling inside and outside Victoria Park on Sunday.
Speaking to reporters after attending a Commercial Radio programme, Executive Councillor Ronny Tong said people should decide for themselves whether to commemorate the June 4 anniversary.
"Hong Kong is a free place. Provided you don't infringe the law, you can do almost anything which will not be harmful to the community at large,” Tong said.
"So I would simply say, 'Be yourself, do what the law allows you to do.'"
But Tong said he does not recommend people to mourn in an organised way, as public events marking the anniversary in the past had been closely tied to slogans used by the now-disbanded Hong Kong Alliance in Support of Patriotic Democratic Movements of China. He said people may interpret the commemoration as a call to end one-party rule.
Last updated: 2023-06-04 HKT 17:04