Full-time ambulance crews were not operating across the southern parts of Down and Armagh during part of the day on Friday.
Local representatives were told that there were no full-time staff working out of the Newry and Kilkeel stations for a time.
The Northern Ireland Ambulance Service (NIAS) said in a statement that staffing issues at the two ambulance stations had "provided us with a challenge" on Friday night.
Sinn Fein MP Mickey Brady said: "I have been informed that there is to be no ambulance cover for Newry, Mourne and south Armagh.
"I have sought urgent clarification from the Trust. If accurate, this is a totally unacceptable situation."
A tenth of the staff were unavailable for work because of Covid-19, which has meant many others have been working overtime, an NIAS spokesperson said.
"This level of overtime is not sustainable and it means on occasions we are unable to provide the planned level of cover in some areas," the statement added.
NIAS said it has plans to cover when operational staff is reduced, including adding crews from other stations, extending Rapid Response Paramedic hours, increasing use of accident and emergency support vehicles and Voluntary and Private Ambulance Services (VAS/PAS).
Southern Area Manager Mark Cochrane told armaghi.com: "It is a source of regret to me whenever ambulance cover is depleted due to a lack of available resources and the potential impact this may have on the community we serve.
"Demand for NIAS services has increased significantly over recent years without a corresponding increase in ambulance resources.
"We are working to address the issue and fill existing vacancies with ongoing regional recruitments and training.
"I would like to express my gratitude to those staff, on the frontline and in ambulance control, who continue to work tirelessly to ensure that an ambulance response is provided to those who have an immediate and life-threatening need."