Raml (walking rapidly) is recommended in the Tawaf of Umrah, and in the first Tawaf of Hajj Sahih Muslim 1264 b
Arabic hadith text
وَحَدَّثَنَا مُحَمَّدُ بْنُ الْمُثَنَّى، حَدَّثَنَا يَزِيدُ، أَخْبَرَنَا الْجُرَيْرِيُّ، بِهَذَا الإِسْنَادِ نَحْوَهُ غَيْرَ أَنَّهُ قَالَ وَكَانَ أَهْلُ مَكَّةَ قَوْمَ حَسَدٍ . وَلَمْ يَقُلْ يَحْسُدُونَهُ .
Translation
This hadith has been narrated on the authority of jurairi with the same chain of transmitters but with a slight variation of words (and this is) that he (the narrator) did not say
" They felt jealous of him. but said: The people of Mecca, were jealous people."