Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
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.”
Said 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.