If the iqaamah for prayer is given during your tawaaf or saa’i, then you should interrupt your tawaaf and pray with the imam, and then complete the tawaaf from where you left off. You do not have to repeat the tawaaf or repeat the circuit which you interrupted in order to pray.
Shaykh Ibn Baaz (may Allaah have mercy on him) said:
If a person interrupts his tawaaf for a reason, such as one who has done three circuits then the iqaamah for prayer is given, so he goes and prays and then comes back, he should start from where he was, and he does not have to go back to the Black Stone; rather he should continue from where he was and complete his tawaaf. This is contrast to what some scholars say, who say that he has to start at the Black Stone. The correct view is that he does not have to do that, as a group of scholars have said. Similarly if a bier is brought in and he offers the funeral prayer, or someone stops him and speaks to him, or there is overcrowding, and so on. Then he should complete his tawaaf and there is nothing wrong with that.
Majmoo’ Fataawa al-Shaykh Ibn Baaz, 17/216
Shaykh Ibn Baaz also said:
If the iqaamah for prayer is given whilst he is doing tawaaf or saa’i, he should pray with the people, then complete his tawaaf or saa’i from where he stopped.
Fataawa Islamiyyah, 2/250.