morituri te salutant or morituri te salutamus is commonly described as the opening rite of a gladiatorial fight.
However, I came across the following in JSTOR (limited access):
Morituri Te Salutamus, H. J. Leon
Transactions and Proceedings of the American Philological Association Vol. 70 (1939), pp. 46-50, about the salute, Claudius' Naumachia on Lake Fucinus, and naumachiae in general.
According to the author, the descriptions of the salute in the Claudian event by Suetonius (morituri de salutant) and Cassius Dio (moriture te salutamus) are the only ancient references to the salute of the gladiators, and it was actually uttered by the naumacharii, as an appeal in the hope of winning the emperor's sympathy. Tacitus is silent on the salute.