“I saw the Messenger of Allah (peace and blessings be upon him) hastening (or running) in the bottom of the watercourse (masīl), and he was saying: ‘The valley should only be crossed by hurrying (shaddan).’”

Narrated by Ahmad (no. 27281), al-Nasā’ī (no. 2980), from a female Companion.
In another narration by Ahmad (no. 27280) and Ibn Mājah (no. 2987): “walks between As-Safā and Al-Marwah.”
Authenticated in Ṣaḥīḥ al-Jāmiʿ (nos. 7553–7554), Silsilat al-Aḥādīth al-Ṣaḥīḥah (no. 2437).

Brief Explanation of the Hadith

Among the pillars of Hajj and ʿUmrah is the Saʿy between As-Safā and Al-Marwah, performed as seven circuits, beginning at As-Safā and ending at Al-Marwah. The Prophet, may Allah’s peace and blessings be upon him, demonstrated its manner through his practice, as he is the one saying: “Take your rituals from me.”
When the Prophet (may Allah’s peace and blessings be upon him) descended from As-Safā heading towards Al-Marwah, he would walk with tranquility. However, when he reached the bottom of the valley (which is the location of the two green markers today), he would hasten his pace, almost reaching a run—which is a quickening of the stride ('adw)—and he would say: “The valley should only be crossed by hurrying (shaddan).”
This hastening in this specific location is a Sunnah for men, but not for women, in order to protect them and block the means to temptation (fitnah).
And whoever among men abandons the brisk walking between the two markers has no blame upon him, for it is a recommended Sunnah, not an obligation. As Sa‘īd ibn Jubayr said: “I saw Ibn ‘Umar walking between As-Safā and Al-Marwah, and he said: ‘If I walk, I have seen the Messenger of Allah walking, and if I hasten, I have seen the Messenger of Allah hastening.’”