Kathir ibn Jumhan said that he saw Sayyidina Ibn Umar (RA) walk during Sa’i. So he asked him, “Do you walk durin Sa’i betw Safa and Marwah?” So, he said, “If I run then I have seen Allah’s Messenger (SAW) also run. And if I walk then, indeed, I saw Allah’s Messenger walk. And I am an old man.”
[Abu Dawud 1905, Nisai 2926, Ibn e Majah 2988]