The two men made speeches in Rome's Capitoline Museum after a signing ceremony on Monday which saw Italian companies tie up 17 billion euros ($18 billion) worth of deals with the Islamic Republic.
A huge statue of Roman emperor Marcus Aurelius on a horse featured prominently in many of the photographs of the event.
But nude statues, including a Venus dating from the second century BC, had all been covered up in temporary wooden cartons, removing the risk of them creeping into any of the shots -- or catching Rouhani's eye.
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"You can not hide your culture, your religion or history itself. It was the wrong decision," Giuliano Volpe, head of the Superior Council for Cultural Heritage at the Italian culture ministry, told public broadcaster Rai3.
"We must enhance rather respect and differences," he said.
The museum cover-up was not the only step Italy took to ensure the Iranian visit passed off smoothly.
As Rouhani refuses to attend official meals at which any alcohol is available, wine was strictly off the menu at both lunch with President Sergio Mattarella and dinner with Renzi.
According to media reports, France has baulked at making a similar placatory gesture, leaving diplomats preparing for Rouhani's visit to Paris from Wednesday with a major protocol headache.