The blaze, which began on Saturday, has burnt through 2,500 hectares of land in the city's southern suburbs.
Some residents had been warned of immediate danger to their lives, but firefighters say the threat has eased.
The New South Wales Rural Fire Service (RFS) described the blaze as "highly suspicious".
"How dare anyone - if they are deliberately involved in lighting fires - endanger our firefighters and also [put] all these communities in harm's way," said Commissioner Shane Fitzsimmons.
The bushfire forced some locals to evacuate their homes on the weekend, while others were told it was too dangerous to leave.
Recent weather in south-eastern Australia has been unseasonably hot, with strong winds fanning bushfires.
Authorities said wind speeds were not as severe on Monday, making it easier to battle the blaze.
Mr Fitzsimmons said flames travelled "right up to the back fences" of houses, but no properties had been lost.
"While the threat has eased, it is still a fairly vigilant fire ground and we want people to remain vigilant," he said.
"There is a lot of work still to be done today and maybe into tonight before we can call the fire contained."
Police have declared the fire a crime scene.
Mr Fitzsimmons said it was possible that winds could strengthen again and elevate the fire danger.
On the weekend, residents hosed down their houses and lawns to prevent embers sparking new blazes ahead of the advancing fire front.
Major roads separating bushland and residences were cut off in some areas, and fire services used helicopters to dump water over key points.
Pictures on social media showed firefighters and residents taking care of local wildlife affected by the blaze.
There has been some amazing work done by firefighter from all agencies. Despite the horrific conditions, there have been no reports of homes being lost. A lot of very hard work still to be done today. @FRNSW #NSWRFS pic.twitter.com/pg0iOMIp8M— NSW RFS (@NSWRFS) April 14, 2018