From John's Gospel we see that this happened before all the women returned to the city. It was occasioned by Mary Magdalene's report, and Peter made this journey not alone, but with John. Mark, after setting forth the angelic message to the women about the Lord's Resurrection, begins to recount the history of the appearances of the Risen One Himself. First of all he tells of the Lord's appearance to Mary Magdalene. But he does not describe in detail the circumstances in which this appearance occurred. He says only that it was the first appearance, and that the disciples did not believe Mary Magdalene's report.
On the first day of the week, while it was still dark, Mary Magdalene comes to the tomb and sees that the stone has been rolled away from the tomb. The thought arises in her that the body of her beloved Teacher and Lord had no rest even in the tomb, but had been carried away. With this sorrowful thought in her soul, she hastily runs to Peter and John, without having inspected the tomb.
On the way she may have met her companions, who were likewise going to the Lord's tomb, and told them her sad supposition. Naturally, she thought that after inspecting the tomb, her companions had come to the same thought concerning the Lord's body. Therefore, when she came to the apostles, she spoke on behalf of all the women: "They have taken the Lord out of the tomb, and we do not know where they have laid Him."
Peter and John rose and ran quickly with Mary to the tomb. Young John ran faster than Peter and came first to the tomb. He, however, did not enter the tomb, but only bent down to see the inside of the tomb. Therefore he could make out only the linen bands lying in the tomb.
When Peter came up, with his usual impetuosity he immediately entered the tomb. John then entered after him. And they saw that the linen bands with which Jesus' body had been wrapped, and the face cloth that had been on His head, lay carefully folded in their places. Their order and appearance clearly indicated that there had been no theft of Jesus' body.
This, however, produced a different effect on Peter and John. The latter saw and believed (Jn 20:8), while the former only marveled within himself at what had happened (Lk 24:12). Having inspected the Lord's tomb, Peter and John returned again to their own place.