Abu Tufayl reported,
I said to Ibn Abbas, "Tell me about this jogging around the Kaaba for three circuits and walking for four. Is it sunnah? Your people claim that it is sunnah."He replied, "They have spoken truly and they have spoken falsely."I asked, "What do you mean by 'they have spoken truly and they have spoken falsely'?"He said, "When the Messenger of Allah ﷺ arrived in Mecca, the polytheists said, 'Muhammad and his companions are too weak and emaciated to circumambulate the House.' They were envious of him. So the Messenger of Allah ﷺ ordered them to jog for three circuits and walk for four."I then asked him, "Tell me about going between Safa and Marwa while riding. Is it sunnah? Your people claim that it is sunnah."He replied, "They have spoken truly and they have spoken falsely."I asked, "What do you mean by 'they have spoken truly and they have spoken falsely'?"He said, "The people crowded around the Messenger of Allah ﷺ, saying, 'This is Muhammad, this is Muhammad,' until even the young maidens came out of their houses. The Messenger of Allah ﷺ would not have people struck aside before him, so when the crowd pressed upon him, he rode. But walking and going briskly on foot is better."
Azami 5002
Sahihعن أبي الطفيل، قال
قلت لابن عباس: أرأيت هذا الرمل بالبيت ثلاثة أطواف ومشي أربعة أطواف أسنة هو، فإن قومك يزعمون أنه سنة؟ قال: فقال: صدقوا وكذبوا! قال: قلت ما قولك: صدقوا وكذبوا؟ قال: إن رسول الله ﷺ قدم مكة فقال المشركون: إن محمدا وأصحابه لا يستطيعون أن يطوفوا بالبيت من الهزال، وكانوا يحسدونه قال: فأمرهم رسول الله ﷺ أن يرملوا ثلاثا ويمشوا أربعا. قال: قلت له: أخبرني عن الطواف بين الصفا والمروة راكبا أسنة هو، فإن قومك يزعمون أنه سنة؟ قال: صدقوا وكذبوا! قال: قلت: وما قولك صدقوا وكذبوا؟ قال: إن رسول الله ﷺ كثر عليه الناس، يقولون: هذا محمد، هذا محمد، حتى خرج العواتق من البيوت. قال: وكان رسول الله ﷺ لا يضرب الناس بين يديه، فلما كثر عليه ركب، والمشي والسعي أفضل.
Muslim narrated it in the chapter on Hajj (1264) from the hadith of Saeed bin Iyas Jariri, Abdullah bin Abu Husayn, and Abdul-Malik bin Saeed bin Abjar, all of them from the hadith of Abu Tufayl. Imam Ahmad also narrated it (2707) from the hadith of Abu Asim Ghanawi, from Abu Tufayl, at greater length than Muslim's version. Abu Dawud also narrated it (1885), though he abridged it. As for this Abu Asim Ghanawi, Ibn Main declared him trustworthy, as noted in Tahdheeb, and Ibn Hibban mentioned him in Thiqat, but Abu Hatim did not know him, and no one narrated from him except Hammad bin Salama. For this reason Hafiz said in Taqreeb, "Acceptable," meaning if corroborated, and indeed he has been corroborated in most parts of the hadith. See the full hadith in the chapter on the reason for pelting the jamarat.As for his saying, "They spoke the truth and they lied," he means they spoke the truth in saying that the Prophet ﷺ performed ramal around the House three times, and they lied in claiming that it is an emphasized, intended sunnah. This is because the Prophet ﷺ did not establish it as a sunnah to be perpetually followed year after year, rather he commanded it that particular year to display strength before the disbelievers, and that reason has since passed. This is the meaning of Ibn Abbas's statement, and it represents his view that ramal is not a sunnah. The majority of the companions, the successors, and those who came after them held that ramal is a recommended sunnah, and that tawaf is valid without it, though one who omits it loses out on its merit, and no atonement is due for it. This is what Umar bin Khattab 
pointed to when he said, "It is something the Messenger of Allah did, and we do not like to abandon it," as will be mentioned later. There is also a report from Ibn Abbas contrary to this, stating that ramal is a sunnah, which will follow.