It is narrated from Hazrat Ata that Hazrat Miswar bin Makhrama performed three circuits (Tawaf) after Fajr, and when the sun rose, he offered two rak'ahs for each circuit. Similarly, after Asr, he performed three circuits, and when the sun had set, he offered two rak'ahs for each circuit.

Ayub narrates that I saw Hazrat Saeed bin Jubair and Hazrat Mujahid perform the Tawaf of the Ka'bah until the sun turned yellow, then both of them sat down (and did not offer the prayer).

Hazrat Aisha (may Allah be pleased with her) says that when you intend to perform Tawaf after Fajr or Asr, then perform the Tawaf, but do not offer prayer before sunrise or sunset, and offer two rak'ahs after every seven circuits.

Hazrat Mu'adh al-Qurashi performed Tawaf with Hazrat Mu'adh bin Afra' after Fajr and Asr, but did not offer prayer.

Hazrat Umar performed Tawaf after Fajr, then mounted his ride and came to the place of Dhat Tuwa and dismounted there. Then, when the sun rose high, he performed two rak'ahs and said: These two rak'ahs have taken the place of those two rak'ahs.

Hazrat Abu Najeeh's father narrates that we offered the Fajr prayer and sat waiting for the Tawaf. Hazrat Abu Saeed Al-Khudri performed the Tawaf, then he sat down and did not offer the prayer.