Commentator William Barclay cites an example of parakaleō from classical Greek that parallels its usage here.
There was a Greek regiment which had lost heart and was utterly dejected. The general sent a leader to talk to it to such purpose that courage was reborn and a body of dispirited men became fit again for heroic action. That is what [parakaleō] means here. It is Paul’s prayer that the Church may be filled with that courage which can cope with any situation. (The Letters to the Philippians, Colossians, and Thessalonians [Louisville, Ky.: Westminster, 1975], p. 129)