All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

Dear brother in Islam, thanks a lot for your question which reflects your care to have a clear view of the teachings of Islam. Allah commands Muslims to refer to people of knowledge to get themselves well-acquainted with the teachings of Islam.

Allah has blessed the Muslim Ummah with a weekly `Eid, which is the Friday congregational Prayer and two yearly `Eids, which are `Eid Al-Fitr(`Eid of Breaking the Fast) and `Eid Al-Adha(`Eid of the Sacrifice). `Eid for Muslims is a time for thanking Allah and getting closer to Him through various acts of worship associated with each `Eid. When one of the two yearly `Eids occur on Friday, this means that two `Eids coincide. As the time for praying `Eid Prayer is so close to the time for Praying Friday Prayer, the Prophet (peace and blessings be upon him) gave permission to those who attend the `Eid Prayer not to attend the Friday Prayer.  

In response to your question, Sheikh `Atiyyah Saqr, former head of Al-Azhar Fatwa Committee, states: 

It is reported that the `Eid occurred on Friday during the time of `Abdullah Ibn Az-Zubayr and thus he stayed in his house till it became noon and then went out, delivered the Khutbah (sermon) and then performed two Rak`ahs and did not perform `Eid. On being asked about this, Ibn `Abbas said: “He has followed the Sunnah.”

Revealing the juristic opinion on this very important issue, we notice that Muslim jurists hold different views. The Hanafis and the Malikis are of the view that when `Eid occurs on Friday, it becomes obligatory to perform both `Eid and Friday Prayer, for one of them cannot replace the other.

The Hanbalis are of the view that he who performs `Eid Prayer can be exempted from performing Friday Prayer. This does not apply to an Imam if there is a sufficient number of people to perform Friday Prayer in which case it becomes obligatory for them to perform it. If the number of people is not sufficient for Friday Prayer, then Friday Prayer is not obligatory. In a narration, Ahmad is reported to have said: “If Friday Prayer is performed at the beginning of the day before noon, then that can replace `Eid Prayer.”

The view of the Shafi`is is that `Eid Prayer is only sufficient for people of villages whose number falls short of those required for Friday Prayer and they have to go to another place, village or town to perform Friday Prayer. They quote the saying of `Uthman Ibn `Affan (may Allah be pleased with him) who said: “O people! You have two festivals in one day. Whoever of the people of `Aliyah (a village near Madinah) wants to perform Friday Prayer with us, can do so, and whoever wants to leave, is allowed to.”

In conclusion, the whole issue is controversial. However, the soundest and the most opinion is that performing `Eid Prayer is sufficient to give one an exemption from performing Friday Prayer. This applies to people residing in rural areas as well as those living in suburban sides. It is also as true for an Imam as it is for an ordinary person.

In his well-known book, Fiqh As-Sunnah, the late Sheikh Sayyed Sabiq states:

If the day of `Eid occurs on Friday, then Friday Prayer is no longer an obligation upon those who performed the `Eid Prayer. Zayd Ibn Arqam said: “The Prophet (peace and blessings be upon him) performed the `Eid Prayer and then made the performance of the Friday Prayer optional, saying: ‘Whoever wishes to pray it may pray it.’”

Abu Hurayrah quoted the Prophet (peace and blessings be upon him) as saying: “Two festivals have occurred together on this day of yours. For whosoever desires, this (`Eid) will suffice for his Friday Prayer, but we are going to perform the Friday prayer.”

It is preferred for the Imam to perform the Friday Prayer so that anyone who wishes to perform it may have chance to do so, as well as those who miss the `Eid Prayer. This is based of the following phrase of the above Hadith: “… we are going to perform the Friday Prayer.”