The HSE carried out over 19,500 COVID-19 tests yesterday - a new daily record.
The executive has capacity for 100,000 a week, but has been facing calls to expand it.
Latest figures show the positivity rate for the testing in the past seven days is over 4%.
Speaking on Newstalk Breakfast, Mr Reid said he's issuing a 'call to arms' for people take recent trends seriously and to act appropriately.
He said: "If anybody's looking at the trends and the numbers coming through right now, it's quite serious.
"If I look at what we did on testing yesterday, we had over 19,500 tests completed yesterday - which is a record from any time we've ever been doing anything.
"That's the volume we're at, the trend we're seeing and that's the concern - people need to now take a radical look at everything we're doing. I really mean it."
He urged people not to meet people they don't need to meet over the next few weeks, and to avoid having others visit their home wherever possible.
Hospitals
Mr Reid said authorities all agree that hospitals are coping for now, but are facing challenges.
There are currently 171 people hospitalised with COVID-19 and 27 in ICU - with Mr Reid saying there's a 'trend upwards' each day.
The HSE CEO explained: "We're all on the same page that our hospital service is challenged, and we're watching it very closely on a daily basis - and we do want to keep all of the other services going."
He said he doesn't believe there's 'any disagreement' between the health service and NPHET, and that they're equally concerned about the impact of a full lockdown - noting that the country is still dealing with some of the impacts of the full lockdown earlier this year.
Mr Reid said there are currently around 41 ICU 'fully-manned' beds available.
There is capacity to scale up capacity if needed - but that would mean stopping some other health services.
Mr Reid added: "We don't want to get near to those levels."
