About 86% of adults in the North of Ireland have had at least one jab for Covid-19.
Mr Swann SAID that hitting the target of 90% would take “pressure off our system”.
He said hospitals were under strain due to the “high numbers of Covid-positive patients coming in”.
“Just over 85% of our adult population is vaccinated – another 5% would see our hospital admissions decrease by 50%,” he said.
“We are seeing the under-40s especially making up high percentages of positive cases – between two thirds and three quarters of those testing positive are in that age group which correlates with low vaccine uptake.”
On Thursday, nine more coronavirus-related deaths were reported in the North.
Another 1,963 people have tested positive for the virus.
About 70% of people with Covid-19 who are in hospital intensive care units (ICUs) have not been vaccinated, said Mr Swann.
“That’s why the importance of vaccination has never been more critical now,” he said.
“I don’t want to sound like a broken record but I will be because if people come out and get vaccinated we see less positive cases, we see less hospitalisations and we see less pressure on our hospital and health service.”
In recent days, healthcare workers have been asked to volunteer to help with proning – the process of turning ventilated patients on to their front to increase oxygen flow to the lungs – in ICUs.
Mr Swann said the volunteers were needed because the health service had increased the number of ICU beds across Northern Ireland.
The minister also confirmed that he had asked officials to seek the services of military medics “in the coming weeks and months” to boost staff numbers in hospitals.
Military medics from the RAF, the Royal Navy and the Army have previously been called in to help on Covid-19 wards.
On Wednesday, the North’s chief scientific adviser Prof Ian Young said the number of people dying with Covid-19 may not hit a peak “for a couple of weeks”.
Stormont ministers are urging young people to get vaccinated on Saturday and Sunday as part of what they are calling the Big Jab Weekend.
Mass vaccination centres, such as the Foyle Arena, will be offering walk-in first jabs for all adult age groups on this Saturday, August 21 and Sunday, August 22.
Foyle Arena will be open both days from 9 am to 7 pm.
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