Around 40 people a day are receiving Covid-19 penalty notices in Northern Ireland as house parties persist during lockdown.
Arlene Foster said it was unbelievable that some "reckless" individuals were still letting their hair down despite the pandemic emergency and post-Christmas restrictions on socialising.
PSNI chief constable Simon Byrne pledged his force would knock on the doors of anyone "blatantly" breaking the rules.
Stormont's First Minister said: "We are all now partners in protecting people and preventing a greater loss of life."
She added: "I find it incredible, frankly unbelievable, that people are still holding house parties at this time when the rest of us are fighting hard to give the rest of us a chance to live."
She said police officers also have a role to put a stop to "reckless behaviour".
Mr Byrne said the vast majority were complying with the rules.
The senior officer warned if people were breaking the regulations and having parties they could expect "firm and swift" enforcement.
He added: "We won't turn a blind eye when people break the rules."
Mr Byrne said while there were people who still clearly want to break the regulations, he questioned whether the focus on enforcement figures was the right thing to do.
He paid tribute to his officers, staff, the health service and the vast majority of the public for complying with the guidelines.
Mr Byrne acknowledged times were tough for those complying and said police wanted to work with people.
He said it was time to dig deep with the prospect of better times on the horizon.
"My plea to every one of you is remembering that what you do today and the choices you make affect the speed with which our life can return to the normality we all cherish," the Chief Constable said.
Meanwhile, Infrastructure Minister Nichola Mallon has announced she has received support from the Executive for her plans to provide a further financial assistance scheme for taxi drivers.
This new scheme will provide £1,500 to taxi-drivers whose insurance did not cover the full six month period of the existing scheme, and will provide further assistance for all drivers from October 1 until the end of this financial year.
The scheme will open in early February.
Details about eligibility requirements and how to apply will be made available as soon as possible, the department said.