Chief Constable Simon Byrne has said the PSNI will be enforcing the laws around social distancing once the Executive agrees what those will be.
He was speaking alongside Assistant Chief Constable Alan Todd during yesterday's Covid-19 press conference at Stormont Castle.
This came as the Public Health Agency earlier announced that another three people have died after contracting coronavirus, bringing the total to 10 in Northern Ireland.
Another 32 people were tested positive for the virus here, bringing that total to 241 cases.
Of those who have tested positive, 90 (37%) were aged 0 to 44; 81 (34%) were 45 to 69, and 70 (31%) were aged 70 or older. Some 104 were female and 137 were male.
Meanwhile, First Minister Arlene Foster stated that the Executive will be working with the PSNI to decide how much the fines will be for those who fail to adhere to social distancing guidelines.
Deputy First Minister Michelle O'Neill also said that employers should "give themselves a shake" if they are refusing to close non-essential businesses.
Speaking yesterday, Mr Byrne explained that there are now just four custody centres currently operating in Northern Ireland, as part of efforts to enhance social distancing.
He added that the PSNI has also introduced a specialist car in each policing district for officers who have been trained and equipped to deal with incidents where people may display symptoms of Covid-19.
Commenting on what the public will see from police in response to the outbreak in the weeks and months ahead, Mr Byrne said: "You won't see vehicle checks to stop people moving around Northern Ireland but clearly, if people don't heed the prudent advice from health about social distance and movement, we have got to keep all our options open to protect the public and to protect the integrity of the health service so they can continue to treat people."
Mr Byrne also said that people have been charged with coughing at police officers and from Monday the PSNI, along with the Public Prosecution Service, will be launching a "nine-point plan" to give officers more support if they have been coughed at or assaulted while on duty.
"I know from commentary both today and before this, there'll be a lot of interest in how we as a police service may want to use new powers to support the efforts around social distancing," he continued.
"I think it's important to stress that discretion and common sense remain at the heart of policing and like the other organisations in Great Britain, we will be adopting a four-point approach to use new powers that come from the Executive.
"Patrolling officers will be told to engage with the public, explain what the new powers are, to encourage people to adopt them and go home or to stop their work.
"Equally, if we have to we will enforce the law once the new powers are with us and are made clear."
Mr Byrne stressed that the PSNI does have necessary stockpiles of personal protective equipment for officers and the force will be monitoring those levels on a daily basis.
Mr Todd also outlined that when a member of the public calls the PSNI, they will now be asked a number of questions to find out if there is a risk of contracting Covid-19.
"If we identify that there is a risk or the possibility of a risk then the control room, with expert guidance, will talk to the call signs before deploying them," he explained. "Police officers are like you and I and everybody else.
"They have families and elderly parents so their concerns are our concerns.
"We as a senior management team are aware of those concerns and we are working absolutely flat out to manage them," he added.
Meanwhile, both Mrs Foster and Mrs O'Neill used yesterday's conference to once again slam employers and businesses who are not adhering to the necessary social distancing guidelines.
Mrs Foster stated that the Health and Safety Executive is currently working on the matter, while Mrs O'Neill told employers to take "responsibility".
"Let me say this to employers today, take responsibility for your workers," stated the Sinn Fein vice-president.
"Today we are still hearing reports about workers being exploited during this public health emergency.
"They are being given no option by their employers other than to go to work whenever it's not safe for them to do so.
"That has to stop, it must stop immediately and shame on any employer that is exploiting their workforce at this moment in time."