The new steps were announced as Iran counted 144 new fatalities from the COVID-19 disease, its highest death toll for a single day in almost three months.
The Islamic republic has refrained from enforcing full lockdowns to stop the pandemic's spread, and the use of masks and protective equipment has been optional in most areas.
President Hassan Rouhani said Iran would have to live with the virus for the "long haul", as he announced the latest measures to combat it.
Mask-wearing would be "obligatory in covered spaces where there are gatherings", he said during a televised meeting of the country's anti-virus taskforce.
According to him, the measure would come into force as of next week, continue until July 22 and would be extended if necessary.
Rouhani said the health ministry had devised "a clear list" of the types of spaces and gatherings deemed high-risk, but he did not elaborate.
He also did not say what the penalty would be for those who fail to observe the measure.
According to deputy health minister Iraj Harirchi, services would not be provided to those without masks in areas such as government organizations and shopping malls.
But implementing the measure may be difficult, as according to Tehran's mayor, many do not wear masks in places like the capital's public transport network, where it is already mandatory.
"Fifty percent of metro passengers wear masks... and even fewer in buses," Mayor Pirouz Hanachi was quoted as saying by the semi-official ISNA news agency.
"We can't forcefully confront people without masks," he added.
'Red' Counties
Iran reported its first COVID-19 cases on February 19 and it has since struggled to contain the outbreak.
The health ministry on Sunday announced 144 virus deaths in the past 24 hours, its highest for a single day since April 5, raising the total to 10,508.
Spokeswoman Sima Sadat Lari also raised total confirmed infections to 222,669, with 2,489 new cases during the same period.
Official figures have shown an upward trajectory in new confirmed cases since early May, when Iran hit a near two-month low in daily recorded infections.
"Considering the rising numbers, I plead with you to definitely use masks outside and in covered places," Lari said.
Iran closed schools, cancelled public events and banned movement between its 31 provinces in March, but the government progressively lifted restrictions from April to try to reopen its sanctions-hit economy.
The economy is starting to suffer under the pressures of the health crisis.
The country's currency, the rial, has hit new lows against the US dollar in recent days, mostly over border closures and a halt in non-oil exports, according to analysts.
The increasing virus caseload has seen some previously unscathed provinces classified as "red"the highest level on Iran's color-coded risk scalewith authorities allowing them to reimpose restrictive measures if required.
According to Rouhani, the measure would also be extended to provinces with "red" counties.
"Any county that is red, its provincial (virus) committee can propose reimposing limitations for a week", which could be extended if needed, he said.
The government launched an "#I wear a mask" campaign on Saturday and pleaded with Iranians to observe guidelines aimed at curbing infections.
One Iranian is infected with COVID-19 every 33 seconds and one dies from the disease every 13 minutes, Harirchi said on Saturday.
Zanjan county in northwestern Iran has already reimposed restrictive measures for two weeks, its governor said in a televised interview.
It followed a "certain indifference from Zanjan residents and as the number of our (virus) deaths picked up again in recent weeks," said Alireza Asgari.
The limitations include closing wedding halls and a ban on funeral events held at mosques, as they can lead to large gatherings, he added.
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