The Prophet ﷺ only walked briskly between Safa and Marwa to show the polytheists his strength.
أخبرنا أبو عمار الحسين بن حريث قال أنبأنا سفيان عن عمرو عن عطاء
إنما سعى النبي ﷺ بين الصفا والمروة ليري المشركين قوته
Bukhari transmitted it in the Book of Hajj, chapter on running between Safa and Marwa, hadith 1649, and Muslim transmitted it in the Book of Hajj, chapter on the recommendation of touching the two Yemeni corners during tawaf but not the other two corners, hadith 1266/241, from the hadith of Sufyan bin Uyayna, through this same chain, and it is in Al-Kubra, hadith 3973.