Answer
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 during the tawaf or sa`i the iqamah for prayer is given, then one should join the prayer and resume tawaf or sa`i after the prayer.
In responding to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
If during the tawaf or sa`i the iqamah for prayer is given, then one should join the prayer and resume tawaf or sa`i after the prayer. He does not need to start fresh; instead, he or she may resume from where they left.
Thus if he did only three rounds, then he should do another four after the prayer (to complete the prescribed total number of seven).
The Prophet (peace be upon him) said, “When the obligatory prayer starts, one must not be engaged in any other prayer.” (At-Tabarani)
Tawaf is like Prayer; hence, while the congregational Prayer starts, he ought to join it.
It is wrong to continue tawaf or sa`i while obligatory congregational Prayer is in progress.
Almighty Allah knows best.