It is reported about Sayyiduna Abu Dharr al-Ghifari (may Allah be pleased with him) that he took hold of a ring of the door of the Ka'bah and said: I heard the Prophet (peace and blessings be upon him) say: "No prayer is to be offered after the Asr prayer until the sun sets, nor after the Fajr prayer until the sun rises, except in Makkah."
Ahmad, and al-Tabarani in al-Mu'jam al-Awsat, recorded it; its chain contains a narrator, Abdullah bin al-Mu'ammal al-Makhzumi, whom Ahmad and others declared da'if (weak). According to one report Yahya bin Ma'in declared him thiqah (trustworthy), and Ibn Hibban (may Allah have mercy on him) also declared him thiqah, saying: "He makes mistakes." Ahmad's remaining narrators are the narrators of the Sahih.
Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) narrates that the Prophet (peace and blessings be upon him) said: "O Banu Abd Manaf! Let me not find you in a state where you have prevented anyone, at any time of the night or day, from circumambulating the House and from praying."
Al-Tabarani recorded it in al-Mu'jam al-Awsat as a narration of Abd al-Karim from Mujahid. If he is al-Jazari, then he is thiqah (trustworthy), and if he is Ibn Abi al-Mukhariq, then he is da'if (weak); and Allah knows best.
Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates that the Prophet (peace and blessings be upon him) said: "O Banu Abd Manaf! O Banu Abd al-Muttalib! If you are made custodians of this affair, do not prevent anyone who circumambulates this House from praying at any hour of the night or day."
Al-Tabarani recorded it in al-Mu'jam al-Saghir and said: "What is meant is that the two rak'ahs of tawaf may be prayed at any time, after the Fajr prayer before sunrise and after the Asr prayer before sunset." The chain of this report contains a narrator, Salim bin Muslim al-Khashshab, who is matruk (abandoned).
Amr bin Dinar said: I saw Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) perform tawaf after the Fajr prayer and then pray two rak'ahs. Then he said: "Praying is disliked only at the time the sun rises, because the Prophet (peace and blessings be upon him) said: 'Indeed, the sun rises between the two horns of Shaytan.'"
Al-Tabarani recorded it in al-Mu'jam al-Awsat, and its chain is hasan (good).