Merseyside Police has "a real difficulty" in answering all critical calls because of budget cuts, says its chief constable.
The force has lost 1,000 officers since 2010 and has to make further cuts of £18m by 2021.
Andy Cooke QPM said "I've never known the force as stretched as it is now in 33 years' experience".
The Home Office said Merseyside had received an extra £500,000 funding since last year.
The chief constable said the loss of officers - the force had 4,500 in 2010 - meant staff were "struggling" to tackle serious crime.
'On the back foot'
"A lot of those police officers previously have been used for proactivity in relation to guns and gangs and all types of criminality," Mr Cooke said.
"We don't have the ability to do that at the moment so we're very much more reactive.
"We've not got that bulk of people to put into those difficult areas and put criminals on the back foot."
He said officers were "working longer hours and working more days with less days off to keep pressure on offenders".
Mr Cooke said he has had a request for extra funding from the government rejected, meaning the force "will have to do things differently".
He said: "If the cuts continue... we will investigate less of the smaller offences and put more resources in the serious issues."
'Cops off the street'
Pete Singleton, chair of Merseyside Police Federation, applauded Mr Cooke for "having the guts to speak out".
He said: "You can't take 1,000 cops off the streets of Merseyside and say it won't have any affect on policing."
Mr Singleton said the force has already had to make £100m ($127m) of savings and it faces £18m more,
"meaning more officers have to go".
He added "politicians should listen to the public who want more cops on the street".
The Home Office said: "The government has protected overall police spending in real terms since the Spending Review in 2015.
"Police forces continue to have the resources they need to cut crime and keep our communities safe.
"This year Merseyside Police is receiving £0.5m more direct resource funding than in 2015/16."