Resting during sa'i is permissible according to the consensus of scholars from all four schools of jurisprudence. A pilgrim may sit down at Safa, Marwah, or anywhere along the Mas'a corridor to rest, drink water, or recover from fatigue without invalidating their sa'i. The continuity (muwalah) of sa'i is recommended (mustahabb) but is not a condition (shart) for its validity according to the majority of scholars.
Sheikh Ibn Uthaymeen explicitly stated that taking breaks during sa'i for rest, water, or to use the restroom is permissible, and the pilgrim resumes from where they stopped. He noted that the Mas'a is a long corridor (approximately 450 meters each way), and performing seven complete laps is physically demanding, especially in the heat. Islam does not impose unnecessary hardship, and resting is a natural and permitted response to fatigue.
If the iqamah for an obligatory prayer is called during sa'i, the pilgrim should stop, join the congregational prayer, and then resume their sa'i from the point where they stopped. Sheikh Ibn Baz confirmed this ruling, adding that resting on Safa or Marwah to make dua (supplication) is actually from the Sunnah, as the Prophet used to make lengthy supplications while standing on Safa and Marwah. The key point is that the pilgrim must complete all seven laps — the breaks in between do not invalidate the previously completed laps.