Raml (walking rapidly) is recommended in the Tawaf of Umrah, and in the first Tawaf of Hajj Sahih Muslim 1262 a
Arabic hadith text
وَحَدَّثَنَا عَبْدُ اللَّهِ بْنُ عُمَرَ بْنِ أَبَانٍ الْجُعْفِيُّ، حَدَّثَنَا ابْنُ الْمُبَارَكِ، أَخْبَرَنَا عُبَيْدُ اللَّهِ، عَنْ نَافِعٍ، عَنِ ابْنِ عُمَرَ، - رضى الله عنهما - قَالَرَمَلَ رَسُولُ اللَّهِ صلى الله عليه وسلم مِنَ الْحَجَرِ إِلَى الْحَجَرِ ثَلاَثًا وَمَشَى أَرْبَعًا .
Translation
Nafi' reported on the authority of Ibn Umar (Allah be pleased with them) that Allah's Messenger (ﷺ) walked swiftly from stone to stone in three circuits and walked (normally) in four.