Can Tawaf and Sa`i Be Interrupted?
Question

Is it permissible to interrupt tawaf or sa`i?
Praise be to Allah.Is it permissible to interrupt tawaf or sa`i?
If a person is performing tawaf (circumambulation around the Ka`bah) or sa`i (between Safa and Marwah), and he comes across a need (e.g., he is thirsty and wants to drink something, or loses someone from his family members and stops to look for him, or becomes tired and wants to take some rest), and if the break was short, then he may continue his tawaf from where he left off . 
Can you interrupt tawaf for prayer?
If the prayer is called and he interrupts his tawaf to pray , the scholars have disagreed on this issue. The most conservative opinion is that when he continues his tawaf, he should not count the last round which he left incomplete.
Can you take a rest in tawaf and sa`i?
The issue of taking a rest in tawaf and sa`i , however, is based on the condition that tawaf and sa`i should be completed contiguously. 
Continuity in tawaf and sa`i
In sa`i, continuity is not a requirement according to the best opinion.
So, if a person is performing sa`i, and he breaks after some of the rounds, and then comes back to complete them, this would be considered permissible. 
However, regarding continuity of tawaf , the scholars have two opinions:

That continuity is mandatory, and that a long discontinuity without due justification nullifies the tawaf.
That continuity is a sunnah, and the tawaf is not nullified even though the break was long. However, it is better to act according to the first opinion. (See Fatawa Al-Hajj Wal 'Umrah by Ibn Baz, p. 80; Al Majmu' by Al-Nawawi, 8/47 and 49; Al-Mughni, 3/414)