When the Messenger of Allah ﷺ performed the initial circumambulation of the Kaaba, he would walk briskly for three rounds and walk normally for four, from the Black Stone back to the Black Stone. Ibn Umar used to do the same.
حدثنا محمد بن عبد الله بن نمير حدثنا أحمد بن بشير ح و حدثنا علي بن محمد حدثنا محمد بن عبيد قالا حدثنا عبيد الله بن عمر عن نافع
أن رسول الله ﷺ كان إذا طاف بالبيت الطواف الأول رمل ثلاثة ومشى أربعة من الحجر إلى الحجر وكان ابن عمر يفعله
Its isnad is sahih. Bukhari transmitted it in the Book of Hajj, chapter on one who performs tawaf around the House upon arriving in Makkah before returning to his house, etc, hadith no. 1617, 1644, and Muslim in the Book of Hajj, chapter on the recommendation of running during tawaf in Umrah and in the first tawaf in Hajj, hadith no. 1261, and others besides them, through routes from Ubaydullah, conveying the same meaning.