Arlene Foster and Michelle O’Neill said they too were worried about the high levels of infection in the Derry and Strabane council area.
The new restrictions, imposed on Monday, “will be tough for many of you but they are necessary”, they said.
The council area has the highest rate of cases per 100,000 in NI.
The new measures introduced in the area include pubs, cafes, restaurants and hotels being limited to opening for takeaway, delivery and outdoor dining.
All museums, galleries and cultural attractions are closed and people are being asked to avoid unnecessary travel.
In their letter, the leaders also said: “We are already seeing hospital admissions increasing rapidly and we must do everything we can to get on top of the situation.
“We are asking you to work with us to save lives.”
They repeated the need for people to limit social contacts, wash hands well and often, keep a safe distance, wear a face covering and download the StopCovid NI app.
Meanwhile, Robin Swann said the health service was facing what was expected to be the “most challenging period in its history”.
The health minister said the “daunting challenge” included rebuilding services, managing the ongoing pandemic and addressing winter pressures.
A new Covid-19 surge plan for the coming months has been published by the Department of Health.
Each of the individual trusts have also published their local plans.
But three-month plans for rebuilding services at trust level, after the first Covid-19 response, have been paused, because of the recent sharp increase in case numbers.
The plan is aimed at limiting the impact of Covid-19 on wider health service provision.
It aims to enable services to continue to meet demand apart from dealing with the virus.
The Surge Planning Framework includes the establishment of what the minister is calling a regional cancer “reset cell”.
It will allow rapid screening, diagnosis and treatment of cancer patients in a clinically-safe setting.
A statement about rebuilding and stabilising cancer services will be published on Wednesday.
Care homes also feature in the framework, to mitigate future transmission in those settings.
The minister told the assembly the rolling programme of testing of care home residents and staff had detected two out of the 28 outbreaks in care facilities currently being overseen by the Public Health Agency.