The Foyle MLA was speaking after a huge spike in cases locally over the Christmas period.
Concerns have been raised however this week that in some instances people were unable to pre-book PCR appointments while others said they could not get lateral flow testing kits.
The Public Health Agency NI yesterday issued new guidelines which stated that only those with symptoms or a positive lateral flow should now book a PCR as pressure mounts on the system due to the virulence of the Omicron strain.
Foyle MLA Mr Delargy said: “Over the Christmas period we have seen increasing numbers of people testing positive and identified as close contacts for COVID19.
“This has resulted in increased demand for PCR test appointments and online orders of lateral flow test kits.
“The increased demand has, however, created a shortage of PCR test appointments and supply of lateral flow test kits.
“This shortage must be addressed as an immediate priority if we are to reduce the spread of the virus and protect our health service and our hard-pressed health workers.”
The Derry politician added: “I also want to pay tribute to the staff at testing centres and laboratories who are working tirelessly throughout this difficult period, work must be urgently undertaken to ensure that these workers’ are properly supported and resourced.”