Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.089A.

Walking between Safa and Marwah is commended, except between the two markers where jogging is encouraged. The hadith of the daughter of Abi Tajrah tells us that the Prophet (peace be upon him) jogged so hard that his lower garment was wrapped around his body.

Thus jogging between these two markers is preferable, but walking is also permissible between them. Sa’id bin Jubair reported: “I have seen ‘Umar walking between Safa and Marwah.” Then he added, “If you want to, you may walk, because I have seen the Prophet (peace be upon him) walking. So, if you want to jog, you may jog, because I have seen the Prophet (peace be upon him) jogging, but I am an old man.” This applies to a male pilgrim only. As for a woman, she is not required to walk fast between these two points. She should walk at her normal pace. Ash-Shafi’i has reported that once ‘Aishah saw some women walking fast whereupon she said to them, “You should follow our example. You are not obligated to jog (while performing Sa’i)”.