Sayyiduna Ibn Abbas (may Allah be pleased with them both) said: "The Messenger of Allah (peace and blessings be upon him) performed raml (walking briskly) in the tawaf of the House of Allah and between Safa and Marwah because the polytheists had seen weakness in him (peace and blessings be upon him) and in his Companions; that is why he (peace and blessings be upon him) performed raml."
Hadith Referenceالمعجم الكبير للطبراني / باب العين / 10912