Executive Council convenor Regina Ip on Sunday said issuing arrest warrants for eight national security suspects living overseas sends a clear message to the world that they have committed "serious crimes".

Chief Executive John Lee has said people should avoid the eight at all cost and that authorities would spare no effort in pursuing them.

Ip told a TV programme that while it's okay for the suspects' relatives to contact them, people offering any form of financial support may get into trouble.

Ip, who's also a lawmaker from the New People's Party and a former security chief, said some fugitives have been organising tea gatherings in places such as the UK to lobby foreign parliament members to sanction Hong Kong. She said such behaviours should be stopped.

In addition to issuing the arrest warrants, police arrested five people last week, accusing the group of supporting overseas activities that endanger national security using money earned through an online shopping platform. Ip said police were not targeting so-called "yellow businesses", but acts threatening national security.

On government plans to implement Article 23 national security legislation, Ip said Hong Kong should enact the law on its own based on its needs and social environment.