Raml (walking rapidly) is recommended in the Tawaf of Umrah, and in the first Tawaf of Hajj Sahih Muslim 1266 b
Arabic hadith text
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، قَالَإِنَّمَا سَعَى رَسُولُ اللَّهِ صلى الله عليه وسلم وَرَمَلَ بِالْبَيْتِ لِيُرِيَ الْمُشْرِكِينَ قُوَّتَهُ .
Translation
Ibn Abbas (Allah be pleased with them) reported
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.