´It was narrated from Jabir bin Abdullah, may Allah be pleased with him, that:` when the Messenger of Allah came down from As-Safa he would walk until he reached the bottom of the valley, then he would hasten until he came out of it.
Hadith Referenceسنن نسائي / كتاب مناسك الحج / 2984
Hadith Gradingالألبانی:صحيح | زبیر علی زئی:إسناده صحيح
The ascent and descent of Safa and Marwah should be traversed at a slow pace, while the low-lying area between the two green lights should be crossed by running. This is the Sunnah.
Source: Sunan Nasa'i: Translation and Benefits by Shaykh Hafiz Muhammad Amin Hafizullah, Page: 2984