This statement was made on Thursday by Alexander Hoffmann, chairman of the CSU parliamentary faction's state group, following coalition talks.
"As a last resort, it was possible to opt for the principle of randomness," Hoffmann said.
The politician added that the coalition had decided to abandon the use of the words "draw" or "lottery."
"Everyone is talking about a draw right now. But it is preferable to talk about the principle of randomness, in accordance with legal advice," he said.
Meanwhile, Hoffmann noted that the proposed "random" system is not considered the only way to replenish the Bundeswehr's ranks.
The German armed forces are currently aiming for 203,000 personnel, but their actual strength has been falling for two years in a row, reaching only about 182,000 by March.