Robin Swann is reviewing guidance on the suspension of hospital visits as lockdown restrictions in Northern Ireland continue to ease.
The Health Minister said he is in the "process" of looking at the matter and will disclose the "revised guidance as soon as is practicably possible".
The development comes as further restrictions here are lifted, with church services able to resume today.
On Friday, caravan parks could reopen, and hair and beauty salons will reopen on July 6, with bars, hotels and restaurants welcoming customers three days earlier.
Yesterday, the Department of Health announced there had been one further death from Covid-19, bringing the death toll here to 550.
For a second day, no Covid-19 patients were receiving treatment in intensive care units. Saturday was the first time it had dropped to this level since health officials began publishing the figure in April.
Mr Swann, responding to a Assembly question asking when hospital visits can resume, said he recognised the "distress and upset" for individuals and families when they cannot visit a loved one who has been admitted, adding it "feels counter-intuitive to how we normally respond in Northern Ireland to family visiting".
"The reduction of visitors to hospitals was a key strategic component of managing the pandemic and it was taken to protect patients, their families, health and social care workers by reducing the risk of infection," he said.
Mr Swann added: "Please be assured that whilst adhering to the principles of the visiting guidance, trusts in Northern Ireland will always consider individual cases to ensure a person centred approach to our service."
He added: "I am in the process of reviewing the Covid-19 visiting guidance, and will share the revised guidance as soon as is practicably possible."
DUP MLA, Paul Frew, who tabled the question, said he felt compelled to raise the issue because an elderly woman in his North Antrim constituency was unable to see her sister during a long stay in hospital.
"There will be many such cases across Northern Ireland and the worry and stress caused to patients can have a detrimental impact upon their health," he insisted.
"We need to see balance in all these decisions.
"The minister has had time to measure and manage risks associated with visitation but the impact of not moving on this issue will be felt hardest by our most vulnerable."