The letter in possession of news channel NDTV asked the IOA to hold fresh elections by Dec 15.
The letter was addressed to senior IOA officials, including acting president Vijay Kumar Malhotra, the channel reported.
India's disgrace in the international sporting arena continued with the IOC refusing to admit IOA into its fold till it keeps away charge-sheeted members from the Indian sporting body.
"The Executive Board heard a report that the IOA's General Assembly had approved most of the amendments to the IOA's constitution requested by the IOC, but one specific clause had not been adopted," said the IOC in a statement on Thursday from the Argentine capital of Buenos Aires.
"This clause, which deals specifically with the eligibility of members, is key to the good governance of the NOC and needs to be fully accepted before the suspended IOA can proceed with the elections. An official notification of the IOC's position will be sent to the IOA," it said.
In Buenos Aires on Wednesday, the IOC said the IOA must adopt the "charge sheet" clause for good governance.
The decision to suspend the IOA was taken first by the IOC in its executive board meeting at its headquarters in Switzerland last year.
The suspension means no Indian national anthem can be played in the international event and the participants cannot contest under Indian flag.
India's sports minister Jitendra Singh said the government will request the International Olympic Committee (IOC) for an alternative solution to enable Indian athletes participate in international meets under national flag.
The Sports Minister told media that it is unfortunate that the IOA is more concerned about its officials' interests than the interest of the nation and the sportspersons.
"It is upsetting that the ban has not be lifted. We have requested for an alternaitive method under which sportspersons can contest under the Indian flag," he said.
Singh earlier in a letter to IOC president Jacques Rogge, had requested it to come up with an interim measure like formation of an ad hoc body so that Indians can participate in international meets under the tricolour.
IOA vice-president Tarlochan Singh speaking to media said the country would be above individuals but has not specified yet what IOA will do to comply to IOC instructions.
"In India we say that after conviction we can debar a person," he had said earlier defending the chargesheeted members of IOA.
--IBNS (Posted on 06-09-2013)