Kit Malthouse MP said new measures were necessary due to rising infection rates and urged the public to report any "situations of major concern".
He spoke during a visit to Staffordshire Police headquarters in Weston Road, Stafford, where he met with new officers brought in as part of the force's latest recruitment drive.
His comments came after the force's Chief Constable Gareth Morgan's announcement that patrols would be stepped up across the county in a bid to clamp down on those flouting lockdown rules.
Mr Malthouse told the Express & Star: "We have a 101 line for people to call if they are very concerned.
"Thousands of people call the police every weekend to complain about noisy neighbours.
"Most people have great relationships with their neighbours and perhaps at first it could be pointed out politely what the rules are.
"I'm sure a lot of people will comply, but if there are situations of major concern then the number is there if people want to use it."
Those who break Covid restrictions – such as refusing to wear a face mask or participating in a large gathering – can be fined £100 for a first offence, rising to a maximum of £3,200 for repeat offenders.
Mr Malthouse said that while enforcement was "necessary" at times, it should only be used as a "last resort".
"We want to educate and encourage people to comply, and in the vast majority of cases what we are finding is that people are following the rules because they recognise the seriousness of the situation," he added.
"Where they are not, then a little bit of encouragement from the police usually means that they do.
"It is only in a very small number of cases that enforcement may well be warranted, with fixed penalty notices handed out.
"In the last lockdown, with a population of 65 million in the country, the police only handed out something like 14,000 to 15,000 penalty notices, which is tiny.
"Most people took the lockdown very seriously and I'm very confident they will do so this time as well."
During his visit Mr Malthouse spoke to new recruits who have joined the force as part of the Government's national drive to bring in 20,000 officers over three years.
He praised the force for being "ahead of schedule" over its allocation of new officers, adding: "The fact 50 per cent of the new recruits are female is fantastic, because we want to see a good mix of young people coming through into policing. It is very energising."
The Minister said the county would see the benefits of the extra officers in the coming years, with Staffordshire Police better placed to tackle crime.
"The connection between police numbers and the level of crime is direct," he said.
"We believe that in the face of changes in crime, such as the rise in drug use and more serious organised crime, an increase in police officer numbers is required to give the cops more capacity to take the fight to the criminals.
"The new officers recruited under our plan will be directed towards refocusing on some of the violence and neighbourhood crime that plagues places like Stafford and elsewhere.
"Happily, we are already seeing the impact. Crime is down across Staffordshire for the second year running, which is great news, and we want to help the police continue that work."
Staffordshire Police is due to recruit more than 200 officers in the current financial year, including 90 from the Government's uplift programme.
Of this number, 36 recruits have joined via the Police Constable Degree Apprenticeship (PCDA) programme in the past week, where they will learn on the job as an apprentice.
Chief Constable Morgan said: “There are now a number of different entry routes which means we can attract people from a range of different backgrounds to join us in policing.
“Our recruits are proud to work here. They are on their first step and have a long way to go, but they are full of pride and enthusiasm and it’s a pleasure to meet them and hear about their different backgrounds.”
He added Staffordshire Police had improved its gender balance but was working hard to encourage more diversity through positive action and working alongside local communities.