Councils in England say there has been a marked improvement in public health since they took over responsibility for delivering services nearly six years ago, despite budget cuts.
The Local Government Association points to a fall in the number of smokers, fewer teenage pregnancies and a decrease in the suicide rate.
But it warns progress could stop if there are further funding cuts.
The government has said councils will get £1.3bn extra next financial year.
The LGA, which represents 370 councils in England and Wales, is calling on the government to reverse budget cuts to councils, which it says would alleviate cost pressures on the NHS.
Councils nationally have had their funding cut by 49% in real terms, between 2010-11 and 2017-18, according to the government spending watchdog.
But the LGA said despite the cuts, councils were enjoying success when it came to public health outcomes.
Since taking over responsibility for public health in England in 2013, testing for sexually transmitted infections was up, while new diagnoses were down.
The rate of teenage conception dropped by almost a quarter from 2013-14, and the number of adults smoking cigarettes in England between 2011 and 2017 fell by about 1.6 million, to 6.1 million.
Overall, councils have maintained or improved 80% of the public health outcomes.
Cllr Ian Hudspeth, chairman of the LGA’s community wellbeing board, said cutting the public health budget was “a false economy” and make it harder to “keep the pressure off the NHS and social care.”
He added that the main public health challenges in England were tobacco use, poor diet, mental health, physical inactivity and substance misuse.
Last month, the government agreed new funding plans for councils in England.
Speaking at the time, Housing and Communities Secretary James Brokenshire, said the financial pot would “pave the way for a more confident, self-sufficient and reinvigorated local government.”