Other than, Naseri said, the man was not showing any visible symptoms of the virus.
Revelations of a new case come after a sailor who caught a repatriation flight from Auckland on November 13 tested positive for Covid-19 in the island nation last week.
Although another test on the sailor came back negative, Samoa was still treating him as a positive case.
Samoa has reported another positive case of Covid-19.
Speaking in Samoan, Naseri said they were still working to figure out exactly where the latest case may have become infected.
Asked whether there was a possibility the man in his 70s may have caught Covid-19 from the first positive case, Naseri acknowledged that did not seem likely.
Two positive cases were on same Air NZ flight
"They were 10 rows apart."
The sailor was seated in row 59, Naseri said, while the older man was in row 49.
"We don't know if [he picked it up] from Melbourne or New Zealand," Naseri said.
"This case - it's not easy as he has [other health conditions]."
The older man and his wife are now in isolation at the country's main hospital, Tupua Tamasese Meaole Hospital at Moto'otua, near Apia.
The sailor and a close contact of his remain in isolation at the same hospital.
Naseri said the two positive cases and their close contacts would stay in isolation at the hospital.
Health authorities were, however, poised to make changes if more cases were identified, he said.
