O'Reilly, who paid €2.27 (£1.62) for each share, has taken his total holding to 207m shares.
The move comes after Denis O'Brien, the Irish telecoms billionaire who holds a minority share in the business, increased his stake to 14.5% last week, after building it up throughout the year.
O'Brien has called for IN&M to sell its loss-making newspapers The Independent and Independent on Sunday, and for O'Reilly to resign.
However, O'Reilly has vowed to resist any proposal to sell off the two national newspapers.
Last week, IN&M issued a trading update for the year ended December 31, which said it expected full-year revenue growth of about 3%, in line with market expectations.
The company said group advertising revenues for papers and online are expected to rise about 4%.
IN&M is the largest newspaper publisher in Ireland but also has investments in Britain, South Africa, Australia, New Zealand and India.