The police in Rome have issued a plea to all of the city’s consulates in a search for the “English speakers” filmed skinny dipping in a fountain at a monument commemorating the unification and liberation of Italy.

The two male tourists stripped to their underwear before getting into the fountain situated at the monumental Altare della Patria, or Altar of the Fatherland, which is also dedicated to all fallen soldiers, a part of the complex including the tomb of an unknown soldier killed in the first world war.

The pair frolicked under the fountain, in Piazza Venezia, before one pulled down his pants and posed for a photo taken by giggling onlookers.

Police said in a statement that the tourists’ behaviour was outrageous and that it “seriously offended the national feeling and the memory of the fallen to whom the monument is dedicated”.

A police source said the men had yet to be traced but if found would each face a fine of at least €400 (£359). They were identified as English speakers by a tour guide, who captured the incident on video. “This enters into the history of Rome … mamma mia … it’s absurd,” he said while filming.

Italy’s hardline interior minister, Matteo Salvini, posted an image of the tourists on Twitter, alongside the message: “I would know how to ‘educate’ these idiots if they get caught, Italy is not their bathroom!”

Tourists jumping into fountains is a persistent problem for Rome authorities, especially during the summer months; although such transgressions are against the law they struggle to control it.

Rome residents get particularly irked by tourists who attempt to recreate a scene from Federico Fellini’s 1960 film La Dolce Vita, in which Anita Ekberg wades into the Trevi fountain.