Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
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If a pilgrim stops during Sa`i for some reason—for example, it is prayer time and he joins the congregation—he may resume his Sa`i when the reason for stopping is no longer there. He should begin from where he left off.
In this regard, Sheikh Sayyed Sabiq states in his well-known book Fiqh As-Sunnah:
Continuity in Sa`i is not a necessary condition of its validity. (However, Malik opines that continuity of Sa`i, without there being a long break, is a necessary condition of its validity.) Thus, if a pilgrim stops performing Sa`i (between Safa and Marwah) for some reason, e.g., it is prayer time and he joins the congregation, in all such cases he may resume his Sa`i when the reason forcing him to stop is no longer there and then begin from where he left off.
It is reported that Ibn `Umar used to perform Sa`i between Safa and Marwah, and whenever he had to answer the call of nature, he would stop, relieve himself, perform ablution, and then go back and resume his Sa`i (reported by Sa`id Ibn Mansur), because continuity in Sa`i is not required.
The author of Al-Mughni observed: “Ahmad said there is no harm in delaying Sa`i after performing Tawaf so that one is rested, or in postponing it until evening. `Ata’ and Al-Hasan also see no harm if someone makes Tawaf early in the day and postpones Sa`i between Safa and Marwah until evening. Al-Qasim and Sa`id Ibn Jubayr agreed with this, because continuity while performing Sa`i is, as such, not a condition, much less continuity of Tawaf and Sa`i.
Sa`id Ibn Mansur reported that Sawdah, the wife of `Urwah Ibn Az-Zubayr, performed Sa`i between Safa and Marwah and because she was a large and heavy woman, she completed it in three days.
Almighty Allah knows best.