The patients' samples have been sent to a laboratory in New Zealand for testing.
The government says the identity of the cases is confidential, despite the first suspected case - since proven negative - being identified in local media.
The ministry of health has urged people to respect the privacy and confidentiality of patients and to avoid stigmatising people who might be affected by Covid-19.
The initial case, an Auckland-based Samoan who had travelled for a birthday, had been threatened and abused online along with her family, after media reported her name and Prime Minister Tuilaepa Sailele Malielegaoi mentioned her village.
Six suspected cases have tested negative so far.