The restrictions on visitors are being reviewed after a backlash from grieving relatives.
Premier Dominic Perrottet said he'd spoken to Sydney woman Gayle Roberts who was made to wait in a hospital car park for five hours while her mother died alone inside Campbelltown Hospital.
"I had tears in my eyes hearing the stories," he told reporters on Wednesday.
"Gayle said to me on the weekend, this will be with her forever.
"I'm incredibly sorry behalf of the state."
Mr Perrottet said the rules have to strike a "difficult balance" between limiting the spread of COVID-19 in the hospital system and making sure family support is available to those gravely ill and dying.
In some hospitals there had been major outbreaks of the virus which had led to more deaths.
"I know we need to be cautious, but my view is compassion overrides caution in these instances," Mr Perrottet said.
"My expectation is that you'll see an announcement very shortly."
While the number of COVID-19 infections recorded across the state have peaked and fallen, the number of people dying with the virus remains stubbornly high.
Twenty new deaths were reported on Wednesday, as well as 10,312 new cases.
Some 1906 people remain in hospital with the virus, with 132 in intensive care of which 61 are ventilated.
More than 1600 people have died in NSW from COVID and more than a million have contracted the virus.
Meanwhile rapid antigen testing in NSW schools is "unlikely" to continue past the fourth week of term, despite filling an important role in the return of children to classrooms.
Mr Perrottet says it's "unlikely" rapid antigen tests will continue beyond the end of February, with the government "assessing what we're going to do from week four (of term) onwards".
More than 3000 people - about 2400 students and more than 600 school workers - tested positive to coronavirus in the first week of term.
Some 43.6 per cent of primary school aged children have received their first dose of a coronavirus vaccine.
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