NI's six health trusts have warned that by the third week of January, NI hospitals could be dealing with double the number of Covid patients.
In a joint statement, the trust chief executives said the figures were based on modelling projections.
They also said there were staffing concerns at a time when there are increased numbers of patients.
Earlier on Sunday night, the Western Health Trust issued an appeal to off-duty staff.
It called for any staff near South West Acute Hospital (SWAH) in Enniskillen, County Fermanagh, to either contact the trust or go to the hospital.
The hospital has additional beds and the staff were wanted so it could help out the Southern Health Trust, which was under severe pressure at Craigavon Hospital and Daisy Hill Hospital.
The Western Trust has since said it was "overwhelmed by the offers of help and support from" staff and that the situation has now stabilised.
It added that it no longer anticipated patients being diverted from Craigavon or Daisy Hill to SWAH.
1/2 We would like to thank all our staff who responded to the staff appeal, issued earlier this evening. We were overwhelmed by the offers of help and support from staff who have already given so much over the past number of months. pic.twitter.com/lufJzII3ct— Western Trust (@WesternHSCTrust) January 10, 2021
Earlier, Western Trust chief executive Dr Anne Kilgallen said NI hospitals are "facing into an abyss."
She added: "We can say that this situation is more grave than it has ever been in the course of this pandemic.
"At the moment one in four of the people in our hospitals have Covid-19. It's about 700 people.
"At the peak of the first surge there were 400 people in hospital so already we're in a very grave situation."
On Sunday there were 703 people in hospital with the virus, 53 people in intensive care units (ICU) and 34 being ventilated.
Pat Cullen, director of the Royal College of Nursing NI, said staff were working "above their contracted obligations, are overworked and overtired".
She added that any attempt to force them to cancel annual leave would be "inhumane".
As nurses enter another week of relentless pressures we all must recognise they are working away above their contracted obligations, are over worked & over tired. Any attempt to force them to cancel their annual leave would be inhumane. They also need some rest.— pat cullen (@patcullen9) January 10, 2021
Earlier, Belfast Trust chief executive Dr Cathy Jack appealed to staff to "voluntarily postpone any planned booked annual leave in the coming weeks".
'Not simply a matter of more beds'
In the joint statement, trust executives urged the public to "stay at home, practise social distancing, hand hygiene and wear face coverings."
In December they warned "several of NI's acute hospitals were operating beyond capacity".
In their latest statement, the trusts said dealing with the pandemic was now "not a simple matter of putting up more beds."
The statement said: "We need the staff to care for the increased number of patients.
"Pre-existing staffing pressures and staff absence because of COVID, and other reasons, mean that those staff simply aren't there."
Seventeen more coronavirus-related deaths have been reported by the Department of Health in Northern Ireland in the past 24 hours.
It takes its death toll to 1,460.
In their statement, the trusts made reference to the standing down all but the most urgent elective surgery, including some red-flag cancer surgery.
"This was to redeploy staff to meet the urgent and immediate needs of extremely ill patients, especially both Covid and non-Covid patients needing ICU care," they said.
The trusts said the postponed operations would be rescheduled as soon as possible.
They added that patients who did undergo surgery may need to travel further for it.
Cancer services are seeking to maintain chemotherapy, radiotherapy and other non-surgical treatments and alternative treatments will be provided in the absence of surgical options.
They said that staff "although exhausted, will once more go above and beyond to do the best they can for as many people as possible, and we thank them for it."
However, the chief executives added that it would not be easy and the "care that we are able to provide will at times fall short of the high standards we normally deliver but we will do our very best."
'Desperately ill patients will be prioritised'
The trusts also warned the public that no-one should be attending a hospital emergency department at any time unless they need emergency care and said longer waits were likely
They added that patients arriving by ambulance will also wait at times, sometimes for many hours before space is available in an already over-stretched ED.
"This has a direct impact on the ability of the Northern Ireland Ambulance Service to respond, in a timely manner, to life threatening emergencies in the community," the statement said.
Vaccination drive continues
The trusts said the vaccines rollout "provides the long-term hope and the current lockdown offers the opportunity to shorten the duration of the current surge."
The Health Department anticipates the vaccination programme will continue until the summer of 2021.
In the Republic of Ireland the Department of Health reported eight further coronavirus-related deaths on Sunday, bringing its death toll to 2,344.
It said there are 6,888 new cases and 125 people are in ICU.
Earlier this week, the reproductive rate of the virus in Northern Ireland - known as the R-number - was sitting at about 1.8.