Musnad Ahmad 25:239

Muhammad ibn Ubayd narrated to us, Fitr narrated to us, from Amir ibn Wathilah, who said: I said to Ibn Abbas: "Your people claim that the Messenger of Allah, peace and blessings of Allah be upon him, performed *ramal* (brisk walking during Tawaf), and that it is a Sunnah." He said: "My people spoke the truth and they lied. The Messenger of Allah, peace and blessings of Allah be upon him, did perform *ramal*, but it is not a Sunnah. However, he arrived while the polytheists were on Mount Qu'ayqi'an, and they were saying that he and his companions were suffering from weakness, exhaustion, and hardship. So he commanded them, and they performed *ramal* around the House (the Kaaba) to show them that no weakness had afflicted them."