It is narrated from Sayyiduna Ibn Umar (may Allah be pleased with them both) that the Prophet (peace and blessings of Allah be upon him) performed ramal (brisk walking) in the first three circuits of tawaf from the Black Stone to the Black Stone.
Hadith Referenceمسند احمد / مسند المكثرين من الصحابة / 6047
Hadith Gradingحکم دارالسلام:حديث صحيح ، خ: 1617، م: 1261، عبد الله العمري - وإن كان ضعيفا- قد توبع.