The home secretary has said police forces in England and Wales should not ask for money from the government when crime goes up, but focus on prevention.
Amber Rudd told a conference of the National Police Chiefs' Council (NPCC) and Association of Police and Crime Commissioners forces should give people a "plan to make them safer" instead.
She said funding decisions would be "based on evidence and not assertion".
NPCC chairwoman Sara Thornton warned the police service was "stretched".
Ms Thornton, speaking at the two-day gathering in London, said offences involving knives, guns and serious violence had increased significantly - warning that the crime climb was not a "blip".
"Could this be the beginning of the end of the great crime decline?" she said.
The number of crimes recorded in England and Wales rose by 13% in the year to June, according to the Office for National Statistics, surpassing five million offences for the first time in 10 years.
Crime categorised as "violent" rose by 19%, with rises in offences including stalking and harassment.
But Ms Rudd, who unveils a police funding settlement later this year, said budget discussions "mustn't just be about lobbying the government for money".
She said: "It needs to be about cutting crime, delivering on the priorities you were elected on and being held to account by local people in your area when you don't.
"When crime stats go up I don't just want to see you reaching for a pen to write a press release asking for more money from the government," she added.
Ms Rudd pointed to the Crime Survey for England and Wales - which is based on people's experiences of crime, not actual reports - and noted a 9% reduction in offences compared with the previous year.
She acknowledged that an increase in complex investigatory work and an unprecedented wave of terror attacks had put pressure on forces.
Latest statistics show that police officer numbers in England and Wales have fallen by 19,000 since 2010.
The NPCC's Ms Thornton said the government's 2015 "flat cash" settlement for forces was "unsustainable".
Police budgets will remain broadly flat in cash terms from 2016/17 to 2019/20, under the current Spending Review.
The conference comes a day after Metropolitan Police commissioner Cressida Dick warned it would be "incredibly demanding" for the force to find another £400m in savings on top of cuts it has already made.