Nasai

519. Commentary: The aforementioned narration is weak in its chain of transmission. However, in the case of performing tawaf after the Asr or Fajr prayer, it is permissible to offer two units (rak‘ahs) of prayer after tawaf, as it is narrated from Jabir bin Mut‘im radi Allahu anhu that the Messenger of Allah sallallahu alayhi wa sallam said: “O Banu ‘Abd Manaf! Do not prevent anyone from performing tawaf of this House and praying at any time of the night or day whenever he wishes.” [سنن أبي داود ، المناسک ، حدیث : 1894]

Therefore, from this Prophetic statement it is understood that performing tawaf in the House of Allah after Asr and likewise after Fajr is permissible. Accordingly, the two rak‘ahs of tawaf in these prohibited times will also be permissible. However, the prohibition of offering unrestricted voluntary (nafl) prayers after Asr and Fajr is established from other ahadith. See: [صحیح البخاري ، مواقیت الصلاة ، حدیث : 586 ، وصحیح مسلم ، صلاة المسافرین ، حدیث : 827]

But obligatory (fard) or missed (qada) prayers may be performed. If the Zuhr prayer remains, it can be offered after Asr as well. If the Sunnah prayers of the morning remain, they can also be offered after the Fajr prayer. Similarly, the two rak‘ahs of Tahiyyat al-Masjid (greeting the mosque) may also be performed. For clarification of this issue, see hadith: 586 and its benefit.