The HSE says direct provision centres are now receiving priority testing.
However, the National Public Health Emergency Team (NPHET) is still deciding whether everyone in them should be tested.
There are 1,700 residents in direct provision centres around the country - 149 had tested positive for the virus as of last Friday.
Dr Breda Smyth from the HSE says the level of testing in them is dependent on the need in each individual facility.
"We have seen a number of outbreaks in direct provision centres and each outbreak is evaluated and a risk assessment is made on each
"So for each risk assessment is decided the testing strategy within that direct provision centre.
"This is a case by case mechanism."