The latest highly publicised act of contrition by Agca came 31 years to the day after John Paul visited him in prison in Rome to forgive him for the 1981 shooting that nearly killed the leader of the world's Catholics.
Agca, then 23, shot the pope twice from close range in St Peter's Square, one bullet passing through his abdomen and another narrowly missing his heart.
He arrived back in Rome unexpectedly on Saturday and presented himself to police to declare his intention to lay the flowers.
Agca requested a meeting with Pope Francis when the current pontiff visited Turkey last month. That was declined as was a fresh request for an audience this weekend in Rome.
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"He has put flowers on the tomb of John Paul II. I think that is enough," Francis's spokesman, Federico Lombardi, told La Repubblica.
The motive for Agca's 1981 attack on the pope remains a mystery. He served nearly three decades in prisons in Italy and Turkey and is widely considered to be mentally disturbed.