Abu al-Tufayl (may Allah have mercy on him) says: I said to Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both): "What is your view: is the tawaf of the House with raml (brisk walking) for three circuits and walking for four a Sunnah? Your people claim that it is a Sunnah." He said: "They have told the truth, and they have lied." I said: "What do you mean by 'They told the truth and they lied'?" He said: "The Messenger of Allah (peace and blessings be upon him) came to Makkah, and the polytheists said that Muhammad (peace and blessings be upon him) and his companions would not be able to perform the tawaf of the House because of weakness, and they used to envy him. So the Messenger of Allah (peace and blessings be upon him) commanded them to do raml for three circuits and to walk for four." He said: I said: "Tell me about the tawaf between al-Safa and al-Marwah: is doing it riding a Sunnah? Your people claim that it is a Sunnah." He said: "They have told the truth, and they have lied." I said: "What do you mean by saying they told the truth and lied?" He said: "The people crowded around the Messenger of Allah (peace and blessings be upon him), saying: 'This is Muhammad (peace and blessings be upon him)!' until even the young girls came out of the houses; and people were not pushed away from in front of the Messenger of Allah (peace and blessings be upon him). When they became too many, he rode; and walking and running are better." [Sahih: Muslim: 1264]
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9378