Both the patients are from Kohima quarantine centre, he said.
The number of active cases in the state now stands at 79 while 100 persons have recovered, the minister said.
A district-wise breakup shows that Dimapur accounted for the highest number of 126 coronavirus positive cases, followed by 31 in Kohima, 9 in Mon, 8 in Peren and 5 in Tuensang.
The remaining six districts have reported no COVID-19 cases so far.
Eighty-five patients have so far recovered in Dimapur, 10 in Kohima and 5 in Tuensang.
According to data provided by the Health and Family Welfare department, over 7,000 samples have been tested in the state till now.
Chief Minister Neiphiu Rio had said on Monday that from a state with no testing facility, Nagaland now has the capacity of analysing 600 samples per day.
The only BSL-3 laboratory at Naga Hospital Authority Kohima was conducting coronavirus tests and 20 TrueNat machines have been installed in other districts for the purpose, he said.
About 470 tests have been done by TrueNat machines and all the samples yielded negative results, the chief minister said.
With the installation of more TrueNat machines, the testing capacity of the state is expected to double by next week, he said.
As part of its efforts to ramp up the testing capacity, the Indian Council of Medical Research (ICMR) had approved the use of TrueNat system for conducting coronavirus tests. NBS MM MM