CPI-M member TK Rangarajan raised the issue in the Upper House while participating in a discussion on the working of the Home Ministry.
"Every Prime Minister in the past, including Atal Behari Vajpayee, has wished the community on Eid. But our Prime Minister has not greeted (them) on Eid after the end of the holy month of Ramzan. Is it fair?" he said.
Reacting to Rangarajan's remarks, Parliamentary Affairs Minister Venkaiah Naidu, who was present in the House at the time, rose and said that Modi had done so.
On Tuesday, a Congress member in Lok Sabha had raked up the issue saying that while Modi had hosted no Iftaar party this Ramzan, he had offered prayers at Nepal's famed Pashupatinath Temple.
Adhir Ranjan Chowdhury had said in the Lower House that while nobody objects to the Prime Minister going from "Pashupatinath to Tirupati", there has been a practice since Independence of Prime Ministers hosting Iftaar gatherings during Ramzan.
The statement had evoked sharp opposition from BJP members with Speaker Sumitra Mahajan saying, "Such personal matters will not go on record. I am sorry... This is not the way.