"The only way to end their destiny of being an abscondee who will be pursued for life is to surrender," Lee told reporters.

Hong Kong police issued arrest warrants for the eight overseas-based activists on Monday, accusing them of national security offences, including foreign collusion and incitement to secession, and offered rewards for information leading to their arrest.

The accused are activists Nathan Law, Anna Kwok and Finn Lau, former lawmakers Dennis Kwok and Ted Hui, lawyer and legal scholar Kevin Yam, unionist Mung Siu-tat, and online commentator Yuan Gong-yi.

The police also offered rewards of HK$1 million ($127,656) for information leading to each possible arrest.

The activists are based in several countries, including the United States, Britain and Australia.

They are wanted under a national security law that Beijing imposed on Hong Kong in 2020.

The United States condemned the move through a U.S. State Department spokesman, who said it set "a dangerous precedent that threatens the human rights and fundamental freedoms of people all over the world."

British Foreign Secretary James Cleverly said his government "will not tolerate any attempts by China to intimidate and silence individuals in the UK and overseas".

Both these countries have criticised the national security law for being used to suppress Hong Kong's pro-democracy movement.

Chinese and Hong Kong authorities say the law has restored the stability necessary for preserving Hong Kong's economic success.

Lee said authorities would continue to "monitor" the actions and behaviour of the eight while overseas, without giving specifics on how authorities would do this.

"We want them to know that we will not sit and do nothing," Lee said, who also appealed to members of the public to provide information on the activists.

The Inter-Parliamentary Alliance on China, a broad coalition of politicians around the world, said in a statement that the move "confirms fears of Hong Kongers abroad and represents a dangerous escalation in Beijing's global war on dissent".

It added that the HK$1 million "bounties" on the eight, could "exacerbate community tensions and are likely to precipitate unacceptable infringements of sovereignty," in the Western democracies where the activists are now based.

(Reporting by James Pomfret and Donny Kwok; Editing by Muralikumar Anantharaman and Raju Gopalakrishnan)

By James Pomfret and Donny Kwok