The Health Minister Simon Harris says the backlog of tests shipped to a German lab for analysis should be completed by the end of next week.
He says between 25,000 and 30,000 were sent and 14,000 have been returned.
It was confirmed on Friday just over 1,000 of those are COVID-19 positive.
The number of coronavirus cases here was revised upwards by the National Public Health Emergency Team (NPHET).
Originally the group said there were a total of 7,054 confirmed cases here as of Friday.
But that number was later revised to 8,089 cases, after some 14,000 samples were returned from German labs.
Of these samples, 1,035 were positive for the virus.
"With the latest German figures included, there are now 8,089 confirmed cases of COVID-19 in Ireland", NPHET said.
Minister Harris says the remaining tests left to be completed will be done over the coming days.
"It is our hope, our expectation and our plan that by the end of next week, any backlog in relation to testing will have been addressed.
"And we want to move to a place where people can get their test results within 48 hours.
"So we built up the capacity here in Ireland to ensure that that's in place in terms of lab capacity, swabs and testing centres.
"And we're dealing with the legacy backlog, if you like - and that will be dealt with by next week".