Firefighters are continuing to battle a blaze that has burnt more than 2000 hectares of bushland in the Royal National Park south of Sydney since Saturday.

An increase in wind on Monday afternoon has produced a significant amount of smoke, mainly over parts of south-west Sydney, the Illawarra and the South Coast, an RFS spokesman said.

The large bushfire at the Royal National Park was burning out of control on Sunday. Credit:Glenn Campbell

Residents are being urged to call triple zero only if they see a fire burning unattended.

Fire crews are patrolling containment lines and continuing to strengthen those lines, and there are no current threats to properties, the RFS said.