Police chief constable Simon Byrne said he was concerned some of Northern Ireland's empty roads were being used as race tracks, warning drivers the coronavirus outbreak will not get them off the hook if they are caught speeding.
Mr Byrne, speaking on BBC Radio Ulster's Good Morning Ulster, said that members of the public have largely been "pretty responsible" in following government advice on social distancing.
It comes after reports of people flocking to beauty spots over the weekend.
New draconian powers came into force on Saturday night allowing the police to clamp down on those found not following health advice on remaining indoors. Crowds of more than two people that are not all from the same household are banned.
It is early days.Simon Byrne
Mr Byrne said police wanted to use the powers as a last resort and would be taking an "engage, explain, encourage and then enforce" approach.
"Like many things in policing we rely on the cooperation of the public to keep things safe," he said.
He said there were a few occasions when the PSNI stepped up patrols in certain beauty spots and they had to advise people to "go home".
There was also one incident when officers had to tell a person who was self-isolating to go back into their home.
"But by and large, people have been cooperative and responsible.... but it is early days," he added.
Mr Byrne also encouraged anyone who has seen people flouting the rules to contact police.
He also said that two officers have been confirmed to have Covid-19, but said the PSNI currently has one of the lowest absence rates of forces in the UK.
He added: "We have people that are coming and going, as maybe other industries and businesses have, that are self-isolating and then coming back to work.
"But as we stand we are the third lowest police service anywhere in the UK for absence in work. That is a tribute to the commitment and energy of our staff to keep the place going because of a sense of duty and public service. I have been hugely impressed."
He paid tribute to his officers on the front line that are continuing to work in and patrol communities across Northern Ireland as well as cleaning staff in stations. He said they were following social distancing where possible and indeed had special patrol units were out with officers in special "head-to-toe" protective gear. Protective equipment for patrols had also been stepped up.
"It is an issue we are taking really seriously because the welfare of our staff is important to keep people at work to keep you safe."
Mr Byrne said they were aiming to put more staff out on patrols right across Northern Ireland with possible cordons in place to ask people why they are out.
"We want to strike a balance," he said, "people need to get out and do their shopping, those essential workers still need to get to work so we have to see that.
"The big thing to stress is we will still be pushing speeding enforcement. There has been a lot of concern and evidence over the last few days some people are treating empty roads like race tracks.
"So we will be there to enforce the law quite robustly because we can't afford to put more pressure on the health service."
Sunday saw the biggest single day increase since the outbreak of coronavirus in Northern Ireland, with six deaths and 86 new confirmed cases.
The death toll in Northern Ireland now stands at 21. Covid-19 related deaths in the UK rose from 1,019 to 1,228 on Sunday, an increase of 209, the second biggest day-on-day rise in the number of deaths since the outbreak began.
Health Minister Robin Swann also advised people to be ultra careful and to try and avoid accidents so as not to put additional strain on the health service.
He also revealed that over 4,000 people had registered an interest in joining Northern Ireland's health and social care workforce during the Covid-19 pandemic.