Beijing: Hong Kong's embattled Chief Executive Carrie Lam has condemned protesters for increasingly violent clashes between police and activists and said she will continue in her role in the wake of a report she offered to resign.

The Financial Times, citing two unnamed sources, said Lam had made several offers to resign as the leader as protest marches brought up to 2 million people onto Hong Kong streets, but the offer was rejected by Beijing.

Protesters have been calling for Lam to resign, and the revelation she has been unable to do so because she answers first to the Chinese leadership in Beijing and not the voters of Hong Kong, is likely to deepen their disillusionment with Hong Kong's political system.

But on Monday, Lam's office denied the resignation report, and she appeared publicly with security minister John Lee to step up condemnation of the protesters.