Musnad Ahmad 25:1633

Yazid narrated to us, informed us al-Jurayri, from Abu al-Tufayl, who said: I said to Ibn Abbas: "Tell me about riding between al-Safa and al-Marwah, for your people claim that it is a Sunnah." He said: "They spoke the truth and they lied." I said: "They spoke the truth and they lied? What is that?" He said: "The Messenger of Allah, peace and blessings of Allah be upon him, arrived in Makkah, and the people came out, even the young women who had reached puberty came out. The Messenger of Allah, peace and blessings of Allah be upon him, was not one to be crowded. So the Messenger of Allah, peace and blessings of Allah be upon him, rode and performed the circumambulation while he was riding. And had he dismounted, walking would have been more beloved to him."