Sahih Muslim 1266
Sahih Muslim · Book 15: The Book of Pilgrimage · Raml (walking rapidly) is recommended in the Tawaf of Umrah, and in the first Tawaf of Hajj
Ibn Abbas (Allah be pleased with them) reported:
وَحَدَّثَنِي عَمْرٌو النَّاقِدُ ، وَابْنُ أَبِي عُمَرَ ، وَأَحْمَدُ بْنُ عَبْدَةَ ، جَمِيعًا عَنِ ابْنِ عُيَيْنَةَ ، - قَالَ ابْنُ عَبْدَةَ حَدَّثَنَا سُفْيَانُ، - عَنْ عَمْرٍو ، عَنْ عَطَاءٍ ، عَنِ ابْنِ عَبَّاسٍ ، قَالَ إِنَّمَا سَعَى رَسُولُ اللَّهِ صلى الله عليه وسلم وَرَمَلَ بِالْبَيْتِ لِيُرِيَ الْمُشْرِكِينَ قُوَّتَهُ .
Allah. 's Messenger (peace be upon him) observed Sa'i and walked quickly round the House with a view to showing his strength to the polytheists.