His statement—may Allah bless him and grant him peace—“When any of you leads the people in prayer, let him keep it brief.” (1) What is meant by keeping it brief is that which conforms to the sunnah.
The evidence for occasional brevity is the Prophet’s statement—may Allah bless him and grant him peace: “I begin the prayer intending to make it lengthy, but then I hear a child crying, so I shorten the prayer, lest I cause hardship for his mother.” (2) Another narration states: “...for fear that his mother might be distressed.” (3)
His statement: “while completing it.”
Its apparent meaning is that completing the prayer is sunnah for the imam. Completion means conformity to the sunnah; it does not mean restricting oneself to the bare minimum that is obligatory. Rather, conformity to the sunnah is completion. However, when we consider the evidence, it becomes clear that brevity in accordance with the sunnah is obligatory for the imam.
The evidence for this is that when Mu'adh ibn Jabal, may Allah be pleased with him, made the prayer lengthy for those praying behind him, the Prophet—may Allah bless him and grant him peace—said to him: “Do you wish, Mu'adh, to put people to trial?” (4) That is, to turn people away from the path of Allah, for trial here means turning people away from the path of Allah, as Allah the Exalted says:
“Indeed, those who persecuted the believing men and believing women and then did not repent—for them is the punishment of Hell, and for them is the punishment of the Burning Fire.” [al-Buruj (The Constellations)]