The Irish Patients' Association (IPA) says health officials need to urgently investigate why so many people are not turning up for their Covid-19 tests.
The HSE said up to a quarter of appointments at some of its centres were not being kept.
Yesterday, 95 more people were reported to have tested positive for the virus with no deaths recorded.
Stephen McMahon from the IPA says all the no-shows could add up to scores of missed cases.
"There's something wrong here that we are not connecting with these individuals to have their tests done," said Mr McMahon.
"So it is the system's failure in that it can't connect with these people to get them back.
"But I think this is really a question for NPHET and the Minister to come up with some solutions to ensure that we can get these no-shows to turn up.
"It is almost 100 people per week that will test positive because of the sheer size of the number of people that are not turning up."
Mr McMahon said it is important that the HSE are able to say what efforts they have made to connect with the individuals not attending their appointments.
"What follow-up are the GPs doing? They are the ones that are making the referrals."