Musnad Abu Ya'la al-Mawsili 110:166

Abu Bakr narrated to us, Abu Mu'awiyah narrated to us, from Ibn Jurayj, from 'Ata', from Ibn 'Abbas, who said: The Messenger of Allah (may Allah bless him and grant him peace) performed *ramal* (brisk walking) during his Hajj and his 'Umrah, as did Abu Bakr, 'Umar, 'Uthman, and the Caliphs after them.