France had ordered a halt to sales of the device, released in 2020, on Tuesday after finding that the model emitted more electromagnetic waves than permitted.
"Apple has assured me that it will implement an update for the iPhone 12 in the next few days," said France's digital minister Jean-Noel Barrot in a statement to AFP.
Both the firm and Barrot insisted there was no danger to public health from the radiation.
"This is related to a specific testing protocol used by French regulators and not a safety concern," Apple said in a statement, adding that the device complied with rules on emissions all around the world.
"We will issue a software update for users in France to accommodate the protocol used by French regulators."
- China woes -
The US tech giant had been given two weeks to issue an update to its phone, which was coming to the end of its career as a front-line Apple product.
Barrot said the agency in charge of testing, the ANFR, would quickly assess the update and decide whether to lift the ban on sales.
The World Health Organization points out that several studies in the field have failed to find adverse health effects caused by mobile phone use.
And there are no specific illnesses linked to such radiation.
But exposure to more than 40 watts per kilogram (W/kg) of electromagnetic radiation does increase body temperature.
European regulations allow only 4 W/kg for such devices and the iPhone 12 exceeded that level by 1.7 W/kg.
Apple has endured an unusually tough week.
Its launch of new products was overshadowed by an announcement that it was replacing its proprietary "lightning" charging ports with standard USB-C ports on the latest generation of iPhones, a measure demanded by EU regulators.
And Chinese officials denied claims that they had banned iPhones in government buildings before taking a swipe at the firm.
Foreign ministry spokeswoman Mao Ning said officials were following "many recent media reports exposing security incidents relating to Apple mobile phones".
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