He was speaking on Thursdays during a visit to the southern Iranian province of Fars.
Einollahi said 63 million of the 68 million shots have been given in the past two months.
Since Wednesday alone, Iranian healthcare workers administered 1,282,823 doses of vaccine to people. The accelerating vaccination process has resulted in a drastic decrease in the number of deaths from Covid over the past weeks.
Iran has seen a downward trend in new infections and hospitalizations as well. But the disease is still killing, though in smaller numbers compared with the time when the fifth peak of the pandemic in Iran was holding a grip on the nation.
Authorities announced on Thursday, Covid-19 has killed 223 more people in Iran in the past 24 hours. The fatalities push to 123,498, the death toll since the pandemic started.
Authorities have lifted some Covid-related restrictions, but they are warning people against relaxing Covid health protocols, saying this could cause a sixth peak of the disease in Iran.