Hilal bin Zayd said: I saw Sayyiduna Anas bin Malik (may Allah be pleased with him), in Hajj and Umrah, walking briskly (doing raml) in the (first) three circuits of the tawaf around the House, and from the Yemeni Corner to the Black Stone he would walk (at a normal pace). Then I heard him say: "This is how I saw the Messenger of Allah (peace and blessings be upon him) do it."
Hadith Referenceالمعجم الكبير للطبراني / باب الألف / 719