The policeman and his female companion, a judge, were on the Spanish Steps late on Saturday night when they were approached by a group of rose sellers, Corriere della Sera said.
After refusing to buy the flowers, they were reportedly attacked by a five-strong group of street vendors. The 48-year-old was hit as the group tried to steal his watch, while his companion, 36, was unhurt.
The policeman’s reaction prompted the gang to flee, leaving the tourists to return to their hotel nearby. Recovering in their hotel room - with a view over the Spanish Steps - the couple noticed that their attackers had returned to sell roses.
The tourists promptly phoned the police who came and arrested three of the men, homeless Bangladeshis aged 22 to 31, although were unable to trace their two accomplices.
The men were sent to the police station and charged with attempted robbery, while the American man was taken to hospital.
The Spanish steps, like other tourist hot-spots in Rome, have become a magnet for insistent and often aggressive street vendors, many of them poor immigrants.
Starting this month, cars have been banned around the base of the steps, a move critics have said will make the area even more attractive to the vendors.