The 49-year-old German-Turk and the 24-year-old Turkish student were praying with a group of foreigners at Venice's main train station and tried to run off when they were approached by a security guard, who then called police.
Police will question the two men, who could face expulsion from Italy, which is on high terrorism alert after a recent wave of attacks, several which were claimed by the Islamic State jihadist group.
In July, IS took credit for an attack by a 17-year-old Afghan asylum-seeker who injured four people on train with an axe and knife in Wuerzburg, southern Germany, before being shot dead by police.
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