The report cited the head of public relations at Iran's Communications Ministry.
The mechanism for how and when Iran would reconnect to the global web following the decision was unknown.
Pezeshkian was responding to a decision by a "special task force" that had previously voted in favour of reauthorising internet access for the population.
No specific date for lifting the blockade has been announced.
In mid-May, Iranian media reported on a possible date of June 5.
Most Iranians have been unable to access the world wide web for 87 days according to the internet observatory NetBlocks on Monday, with only a few citizens having access to expensive and advanced VPNs that circumvent the restrictions.
Authorities initially imposed an internet blackout from January 8 in response to anti-government protests, with connections gradually getting back to normal in February, before a new blackout was initiated following the start of US and Israeli strikes against Iran on February 28.
Since then, the roughly 90 million Iranians have only been able to use the so-called "national internet" in which only state-approved websites can be accessed.
In normal times, access to the global internet remains heavily restricted via censorship of many websites while authorities are increasingly relying on an intranet to provide connected services without relying on the world wide web, notably for schools which are currently following an online curriculum.
The shutdown has had major economic consequences as well as social ones.
More than a million online traders in the country were badly affected, with their income severely restricted by the blockade.
The state officially justifies the shutdown by citing security concerns.
with DPA
