The Chair of the Irish Muslim Peace and Integration Council has written to the Taoiseach to highlight the impact the deferral of Phase 4 will have on the Muslim celebration of Eid at Croke Park.
Dr Umar Al-Qadri has sought an exemption from Taoiseach Mícheál Martin, similar to "the precedent set" by former taoiseach Leo Varadakar.
Last month, an exemption was granted to allow up to 100 people gather in churches and mosques where social distancing is viable.
In a tweet, Dr Al-Qadri said that "Croke Park can certainly accommodate 500 people while maintaining social distancing".
He has expressed hope that Mr Martin will find the basis of dispensation for the special occasion, which he said will mark diversity and inclusivity in Ireland.
On Monday, it was announced that Croke Park would host Eid al-Adha
The 'Festival of Sacrifice' is one of the most important festivals in the Muslim calendar.
It will take place on 31 July or 1 August, depending on the moon sighting.