The nationality of the two people infected is not clear, and no other details were provided.
Ali Aghazadeh said the person was also suffering from a heart problem. It was not immediately clear whether the sixth fatality was among those 10.
A Covid-19 outbreak in Iran, which has so far seen four people die, began in the Shi'ite Muslim holy city of Qom, authorities in Iran said.
Iran holds a parliamentary election on Friday, with many voters expected to visit polling stations.
Chinese Foreign Ministry spokeswoman Hua Chunying said earlier this month that Iran had sent three million face-masks to China and expressed readiness for rendering more medical aid to combat the coronavirus. Authorities reported two deaths previously this week.
IRNA quoted Alireza Vahabzadeh, an adviser to the country's health minister, as saying that both victims had been carrying the coronavirus and were located in Qom, about 140 kilometers (86 miles) south of the capital Tehran. That's where the first two elderly patients died on Wednesday. She did not elaborate. There was no decision so far to suspend flights coming from Tehran, a source at Beirut airport said.
"One of the new cases has unfortunately passed away", he added, noting that 8 of them had been hospitalized in Qom and 2 in Tehran, without specifying where the death occurred.
Qom is a centre for Islamic studies and pilgrims, attracting scholars from Iran and beyond.
Elsewhere in the region, Saudi Arabia announced that citizens and residents of the kingdom are not permitted to travel to Iran following the spread of the virus there.
Iran's health minister, Saeed Namaki, said the roughly 60 Iranian students evacuated from Wuhan had been quarantined upon their return to Iran and were discharged after 14 days without any health problems.