It was the fourth straight day that the daily caseload had topped 3,000. The previous high was 3,186, recorded on March 30, at the height of the initial outbreak.
Health Ministry spokesman Kianoush Jahanpour said that 59 people had died of COVID-19 over the previous 24 hours, taking the death toll to 8,071.
He said that the surge in new cases might be the result of wider testing rather than a second wave of infection.
According to him Iran had now conducted more than a million tests.
A total of 164,270 people have tested positive for the virus.
Infections have been on a rising trajectory in the Islamic Republic of Iran since hitting a near two-month low on May 2, though the official number of daily deaths has remained below 100 in recent weeks.
Health Minister Saeed Namaki on Tuesday lamented that people were ignoring social distancing rules.
"The fact that people have become completely careless regarding this disease" was of great concern, he said.
"They either have total confidence in us or think the coronavirus has gone. The latter is not true at all," the ISNA news agency quoted him as saying.
Nine of the country's 31 provinces are still under a "health alert," Jahanpour said Wednesday, while the southwestern province of Khuzestan remains classified as a "red zone."
Iran has since last month largely lifted the curbs it imposed to stem the outbreak, but experts both at home and abroad have voiced skepticism about its official figures, saying the real toll could be much higher.