The Kebra Negast states that when Menelik I visited his father King Solomon in Jerusalem, Menelik expressed to his father the desire to take to his country the Ark of the Covenant, which is the Tables of the Law that God had given to Moses and that had journeyed through the ages with the children of Israel until they aquired kings to rule over them.

Queen Makeda
Now this Ark rested in possesion of King Solomon and Zadok, the high priest, who was the chief among the priests of Israel who ministered before the Ark in the Temple. The Ark was still in place wherein the power of God rested, and whenever the clergies made their supplications to God, provided it was in accordance with the will of God, the Ark would rise from where it lay. It was the Will of God that the Ark be transferred to Ethiopia.
(Abba Yesehaq)