The Messenger of Allah ﷺ only walked briskly around the House and between Safa and Marwa to show the polytheists his strength.
إنما سعى رسول الله ﷺ بالبيت وبين الصفا والمروة ليري المشركين قوته.
Narrated by Bukhari in the book of Hajj (1649), and Muslim in the book of Hajj (1265:241), both from the hadith of Sufyan, from Amr (that is, Ibn Dinar), from Ata, from Ibn Abbas, as mentioned. Tirmidhi said following the hadith of Ibn Abbas, "This is what the people of knowledge recommend, that one should perform sai between Safa and Marwa, but if one does not run and merely walks between Safa and Marwa, they consider it permissible."In Ibn Abbas's statement, "The Messenger of Allah ﷺ only performed sai around the House and between Safa and Marwa," there is an indication that Ibn Abbas did not consider sai to be a sunnah. He stated this explicitly, as in Sahih Bukhari, mentioned as a suspended report (3847), on the authority of Kurayb, the freedman of Ibn Abbas, that Ibn Abbas said, "Running through the bottom of the valley between Safa and Marwa is not a sunnah, rather the people of the pre-Islamic era used to run there, saying, 'We cannot cross the Batha except at a fast pace.'"Abu Naeem connected this report with a full chain in his Mustakhraj, as mentioned by Hafiz in Taghliq Taliq (4/85). This statement from Ibn Abbas contradicts the position held by the majority of the people of knowledge, who hold that sai is obligatory. Some scholars have held that it is a confirmed sunnah, and that whoever omits it must compensate with a blood sacrifice. This is the view of Abu Hanifa, and it is one of the two views attributed to Ahmad.The meaning of his statement, "We cannot cross the Batha except at a fast pace," is that they would not cross it except by running swiftly, and the Batha is the bed of the valley through which water flows.