International Olympic Committee president Thomas Bach refused to rule out standing for another term as several members called Sunday for a change of rules that would let him extend his time in office.
The German was elected for a first eight-year term in 2013 and re-elected for a further four-year spell in 2021.
Allowing the 69-year-old former Olympic fencing champion to remain in the post beyond 2025 would require a change to the Olympic Charter.
Nevertheless, there were several calls for Bach to continue during Sunday's opening day of the 141st IOC Session in Mumbai.
Luis Mejia Oviedo, the president of the Dominican Republic Olympic Committee, hailed Bach's speech during Saturday's opening ceremony when he announced plans to look at creating an eSports Games.
Oviedo, lauding Bach's response to Russia's invasion of Ukraine, said the IOC needs to "rely on the leadership which you have shown".
Paraguay's Camilo Perez Lopez Moreira urged Bach to run for a further four years, saying the IOC needed his "peaceful leadership".
Djibouti's Aicha Garad Ali added she was speaking "on behalf of Africa" in calling for a charter amendment.
International Gymnastics Federation president Morinari Watanabe told Bach "I love you" as he professed admiration for his leadership.
Watanabe, who is Japanese, however, repeatedly insisted the IOC "must be a role model" for international federations when it came to "good governance".
He also warned about the dangers of "corruption" and a "negative image", in what appeared to be a reference to Sepp Blatter having to resign as president of football's global governing body after being re-elected to a fifth term in the middle of the 2015 'FIFAgate' scandal.
IOC vice-president John Coates of Australia said no alteration to the existing rules could take place in Mumbai because any proposal to amend the Charter must be submitted 30 days before a session, and first requires consideration by the IOC's executive board.
Bach responded by saying he was "loyal to the Olympic Charter" but did not rule out agreeing to an amendment that would allow him to run again.
"Thank you very much for your kind words of support, because I think these words of support are not only directed to me, they are directed to all of us," he said.
Bach added the expressions of support for his leadership went "straight to my heart".
"I always appreciate this support, friendship and the love expressed by Mr Watanabe," Bach said.
Nevertheless, he added: "Having said this, you also know I am very loyal to the Olympic Charter. Being a core author of this Olympic Charter drives me to be more loyal to this Olympic Charter.
"You have heard the explanation of the chair of our legal commission (Coates) in this direction."
- 'No decision has been made' -
At a press conference following Sunday's session, IOC spokesman Mark Adams defended Bach's decision not to close down any debate by simply saying he had no intention of standing again.
"Inevitably, those who don't like us will criticise us," said Adams.
"But I think in an open session, where members and representatives of other members make a point, it needs to be fully considered and not dismissed out of hand.
"No decision has been made. John Coates made some clarifications on the Charter.
"But I think it would be strange if we were to deny members the right to raise points that they thought were important to them.
"Whether you or I think they are not that's another question. They will, I guess, be discussed later on in a considered manner as they should be."
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