On Tuesday Iran state television aired a report from medical reporter Afruz Eslami.
She cited research from Tehran's prestigious Sharif University of Technology.
If Iranians take precautions, they estimate 120,000 COVID-19 cases and 12,000 deaths.
If people comply somewhat with guidance, they estimate 300,000 cases and 110,000 deaths.
But if people don't follow any guidance, Iran's strained health system could collapse.
This could result in 4 million cases, and 3.5 million deaths, Eslami said.
The report aired hours after some Shiite faithful pushed their way into the courtyards of two major shrines that were closed, the AP reported.
As of Tuesday, Iran has seen 16,169 COVID-19 cases, 988 deaths, and 5,389 recoveries.
Iran has the third-highest number of coronavirus cases behind China and Italy.