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According to most scholars, purification is not necessary for performing Sa`i between Safa and Marwah. It is preferable, however, to be in a state of complete purity while performing various rites of Hajj or `Umrah because cleanliness is commendable in Islam.
In this regard, we will cite what Sheikh Sayyed Sabiq states in his well-known book, Fiqh As-Sunnah:
Most scholars are of the opinion that purification is not necessary for performing Sa`i between Safa and Marwah, in light of what the Prophet (peace and blessings be upon him) said to `A’ishah once when she began to menstruate. He told her: "You may perform all the rites (of Hajj) as other pilgrims do, except performing tawaf around the Ka`bah which you may do after you are clean and no longer menstruating." (Reported by Muslim)
`A’ishah and Umm Salamah said: "A woman who performs tawaf, offers two rak`ahs (by the Station of Ibrahim), and then finds that her period has started, may perform Sa`i between Safa and Marwah.'' (Reported by Sa`id ibn Mansur)
It is preferable, however, to be in a state of complete purity while performing various rites of Hajj or `Umrah because cleanliness is commendable in Islam.