The trust said inpatients are only allowed one visit per patient each day, lasting no more than one hour, at hospitals including Altnagelvin in Derry.
A spokesperson said the limitations would be reviewed on Monday, April 11.
Plans are currently underway for a full resumption of visiting arrangements.
But the trust said Covid transmission rates “remain high in the community” and that its staff continue to face “challenges and pressures on our hospitals”.
It also warned that Altnagelvin Hospital was “operating at over 100 per cent capacity” and called for families of recovering inpatients to assist in ensuring a “prompt discharge” in order to free up beds.
Figures out yesterday for Monday showed that in those previous 24 hours there had been a further 108 Covid-19 cases in the Derry City and Strabane District Council area, a rise of 41 on figures for Sunday.
Over the past seven days, there were 615 recorded in the Derry and Strabane Council area.
The infection rates within Derry and Strabane is now the fifth lowest of all 11 councils in the North of Ireland with 407 cases per 100,000.
There were 38 people being treated in Altnagelvin Hospital with Coronavirus and no persons with Covid-19 are in intensive care.
The figures show that 11.20 per cent of beds in Altnagelvin Hospital are occupied by people with Coronavirus and it is running at 8.96 per cent over capacity for beds.
The Department of Health Covid-19 dashboard will be updated today at 2 pm.
In a video posted to social media by the trust, Altnagelvin A&E consultant Ryan Smyth outlined how staff were facing pressures caused by demand and pleaded for the public to have “patience”.
The trust spokesperson added of the visiting limit: “Staff absences due to Covid-19 and other sickness together with a sustained number of Covid-19 patients and…outbreaks in our hospitals must continue to be managed.”
Meanwhile, the north’s Department of Health has recorded a further four Covid deaths and 1,387 new cases.
The department said yesterday there were 530 Covid inpatients in hospitals, of which six required intensive care.
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