The men were caught on camera frolicking in the fountain at the Altare della Patria, with one pulling down his underwear and posing for photos.
The video shows some passers-by laughing and taking photographs, while others can be seen shaking their heads and appearing to tell the two men to get out of the fountain.
The footage has sparked outrage across Italy, and local officials called the act “illegal and offensive”.
League leader Matteo Salvini took to Twitter to condemn the duo’s behaviour: “I will know how to educate these idiots if they are caught. Italy is not their bathroom.”
Rome’s deputy mayor Luca Bergamo echoed Salvini’s anger, stating that the men’s actions “offend each of us, the memory of our country and the fallen, to whom the monument is dedicated”.
“Once identified by the local police, who are actively working to track them down, they will get the maximum punishment possible,” Bergamo added.
Rome’s Altare della Patria is a monument in honour of the first king of Italy following the country’s unification and liberation.
The 19th century monument also holds the Tomb of the Unknown Soldier, commemorating all fallen soldiers.
Roman police are appealing for witnesses to identify the bathers, and have asked consulates in the city to do the same.
If found, the culprits will face a hefty fine.
Skinny-dipping in Italy’s historic fountains is no novelty.
In July 2016, three young women decided to beat the sweltering Roman summer by leaping into Rome’s 17th-century Fontana dell’Acqua Paola.
This year, two Scottish men were fined a staggering €900 for taking a swim in the Trevi Fountain on St Patrick’s Day.
In April, a man was fined €500 for frolicking in the same fountain, perhaps the Eternal City’s most famous.
