The move, a compromise negotiated by N. Srinivasan at an emergency meeting in the southern city of Chennai, appeared unlikely to quell the controversy which has seen the country's sports ministry call on him to resign.
Srinivasan's son-in-law Gurunath Meiyappan was arrested on May 24 for allegedly taking part in illegal betting on the Indian Premier League (IPL) which is the subject of multiple police investigations.
Meiyappan is a business executive for the most successful IPL franchise, the Chennai Super Kings, which is owned by 68-year-old businessman Srinivasan who has headed the Board of Control for Cricket in India (BCCI) since 2011.
'No one asked me to resign'
"Mr. N. Srinivasan announced that he will not discharge his duties as the president of the board till such time that the probe is completed," said a statement after the meeting.
It said Jagmohan Dalmiya, a controversial former president of the BCCI from 2001-2004, "will conduct the day-to-day affairs of the board" during Srinivasan's absence.
The BCCI met Sunday amid growing rancour among the 31-member body and a series of resignations over previous days, including the secretary, the treasurer and the chairman of the IPL, Rajeev Shukla.
Srinivasan described his decision to step aside "an extraordinarily fair step", saying the meeting was smooth and free from acrimony.
"After discussions, I announced I will not discharge my functions till the probe is completed. The decision was well received," he told NDTV station.
A top BCCI official who did not want to be named told AFP the decision was not unanimous.
"I heard Mr Srinivasan say the decision was unanimous... it was anything but unanimous and all I can say at this time is that the last has not been heard about this," he said.
The scandal in the money-spinning IPL, a Twenty20 tournament which sees top international stars play alongside domestic players, has again shaken the faith of fans in what is overwhelmingly India's most popular sport.
The arrest of Srinivasan's son-in-law came after Test paceman Shanthakumaran Sreesanth and two teammates in the IPL's Rajasthan Royals -- Ankeet Chavan and Ajit Chandila -- were taken into custody. All the accused deny any wrongdoing.
Police allege the players deliberately bowled badly in exchange for tens of thousands of dollars after striking deals with bookmakers.
Meiyappan, who is still in custody, is being investigated for allegedly passing information to bookies and placing bets on the IPL. This is illegal under India's laws which ban gambling on all sports except horse-racing.
Srinivasan can only be impeached if three-quarters of the BCCI board vote against him.
Speaking at a defiant press conference last month, he launched a blistering attack on the Indian media's relentless coverage of the scandal.
"I have explained it many times, I have done nothing wrong," he said at the time. "I will not allow myself to be railroaded, bulldozed or threatened."
Cricket analyst Prem Panicker told AFP that Srinivasan should take responsibility for the problems in Indian cricket.
"For two successive years, we have had the taint of match-fixing impact IPL," he said.
"He has failed in pretty much every respect... I can't think of a single area where he got it right," he said of Srinivasan.
The crunch meeting of the BCCI came after IPL chairman Shukla said on Saturday he was resigning from his post "in the best interest of cricket".
BCCI board member I.S. Bindra, the president of the Punjab Cricket Association, said in a statement on Saturday that "this is the worst crisis faced by Indian cricket".
He added: "My central postulate is that the sanctity and credibility of the game should be our focus and be preserved at all costs. The game is bigger than any individual."
India is world cricket's financial powerhouse, accounting for nearly 70 percent of the game's global revenues.
In his time at the top, Srinivasan has shown himself willing to flex India's muscles, even at the cost of unpopularity abroad.
Under his leadership, India resisted the Umpire Decision Review System (UDRS), ignoring complaints from other national boards which favoured the introduction of new technology.
The multi-billion-dollar IPL has changed the landscape of world cricket with its mix of sport, Bollywood glamour, and American-style cheerleaders and television advertising breaks.
While it makes big money, the annual tournament has been dogged by allegations of corporate corruption, money-laundering and tax evasion, as well as secret deals to hide teams' real owners.
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