Eight national security suspects living overseas will be pursued by the Hong Kong authorities for life and anyone with information on them, including their families, should hand it over to the police, Chief Executive John Lee said on Tuesday.

The only way the eight can escape living in fear of arrest every day of their lives is to turn themselves in, Lee added.

On Monday, the police offered rewards of HK$1 million for information that leads to the capture of Dennis Kwok, Nathan Law, Ted Hui, Mung Siu-tat, Kevin Yam, Finn Lau, Anna Kwok and Yuan Gong-yi. They're accused of various offences, including inciting secession.

At a media briefing before this week's Executive Council meeting, Lee said the police move sends a strong message that officers won't sit idly by while people "endanger national security".

"It's just not that this is an important duty they should do, but it is to try to get as much assistance as possible from law-abiding citizens. A lot of them feel a strong responsibility to protect national security, and I think they'll be very pleased to provide information to the police," Lee said.

"I also want to tell the [alleged] criminals that the only way to end their destiny of being abscondees who will be pursued for life is to surrender."

The eight wanted people are living abroad in countries including the United States, Britain and Australia.

"Extraterritorial power exists in many countries' national security law. Hong Kong's national security law is one of the many laws in other countries that will have the same power of taking extraterritorial action against criminals who have contravened their country's law in this regard," Lee said.

He also warned that the government's desire to protect national security won't be swayed by anything foreign politicians have to say on the matter.

"I am not in any way troubled by any attempt to sabotage our action, because I have strong faith that the Hong Kong police will be able to do what they can. I'm not afraid of any political pressure that is put on us, because we do what we believe is right."

In a statement, the Security Bureau said countries that try to excuse the suspects are despicable and have completely disrespected the rule of law.

A spokesperson for the bureau said no countries should harbour criminals.