I said to Ibn ʿAbbas (Allah be pleased with them): Do you think that walking swiftly round the House in three circuits, and just walking in four circuits is the Sunnah (of the Holy Prophet), for your people say that it is Sunnah? Thereupon he (Ibn ʿAbbas) said: They have told the truth and the lie (too). I said: What do your words "They have told the truth and the lie (too)" imply? Thereupon he said: Messenger of Allah ﷺ came to Mecca and the polytheists said that Muhammad and his Companions had emaciated and would, therefore, be unable to circumambulate the House; and they felt jealous of him (the Holy Prophet). (It was due to this) that Messenger of Allah ﷺ commanded them to walk swiftly in three (circuits) and walk (normally) in four. I said to him: Inform me if it is Sunnah to observe Tawaf between al-Safa and al-Marwa while riding, for your people look upon it as Sunnah. He (Ibn ʿAbbas) said: They have told the truth and the lie too. I said: What do your words "They have told the truth and the lie too" imply? He said: When Messenger of Allah ﷺ had come to Mecca, there was such a large gathering of people around him that even the virgins had come out of their houses (to catch a glimpse of his face). And they were saying: He is Muhammad; He is Muhammad. Messenger of Allah ﷺ (was so gentle and kind) that the people were not beaten back (to make way) in front of him. When there was a throng (of people) around him, he rode (the she-camel). However, walking and trotting are better. (Using translation from Muslim 1264a)   

قُلْتُ لِابْنِ عَبَّاسٍ أَرَأَيْتَ هَذَا الرَّمَلَ بِالْبَيْتِ ثَلَاثَةَ أَطْوَافٍ وَمَشَى أَرْبَعَةً أَسُنَّةٌ هُوَ؟ فَإِنَّ قَوْمَكَ يَزْعُمُونَ أَنَّهُ سُنَّةٌ قَالَ فَقَالَ صَدَقُوا وَكَذَبُوا قَالَ قُلْتُ مَا قَوْلُكَ صَدَقُوا وَكَذَبُوا؟ قَالَ إِنَّ رَسُولَ اللهِ ﷺ قَدِمَ مَكَّةَ فَقَالَ الْمُشْرِكُونَ إنَّ مُحَمَّدًا وَأَصْحَابَهُ لَا يَسْتَطِيعُونَ أَنْ يَطُوفُوا بِالْبَيْتِ مِنَ الْهَزَلِ قَالَ وَكَانُوا يَحْسُدُونَهُ قَالَ فَأَمَرَهُمْ رَسُولُ اللهِ ﷺ أَنْ يَرْمُلُوا ثَلَاثًا وَيَمْشُوا أَرْبَعًا قَالَ قُلْتُ أَخْبِرْنِي عَنِ الطَّوَافِ بَيْنَ الصَّفَا وَالْمَرْوَةِ رَاكِبًا أَسُنَّةٌ هُوَ؟ فَإِنَّ قَوْمَكَ يَزْعُمُونَ أَنَّهُ سُنَّةٌ قَالَ صَدَقُوا وَكَذَبُوا قَالَ قُلْتُ مَا قَوْلُكَ صَدَقُوا وَكَذَبُوا؟ قَالَ إِنَّ رَسُولَ اللهِ ﷺ كَثُرَ عَلَيْهِ النَّاسُ يَقُولُونَ هَذَا مُحَمَّدٌ هَذَا مُحَمَّدٌ حَتَّى خَرَجْنَ الْعَوَاتِقُ مِنَ الْبُيُوتِ قَالَ وَكَانَ رَسُولُ اللهِ ﷺ لَا يُضْرَبُ النَّاسُ بَيْنَ يَدَيْهِ قَالَ فَلَمَّا كَثُرَ عَلَيْهِ رَكِبَ وَالْمَشْيُ وَالسَّعْيُ أَفْضَلُ لَفْظُ عِمْرَانَ