The purchase, announced to the Irish Stock Exchange last night, came after IN&M put out a statement claiming O'Brien's actions were "designed to destabilise the company" and that he was "not acting in the best interests of all stakeholders".
O'Reilly has bought a further 10m IN&M shares, priced at €1.86 each, at a total cost of €18.6m (£14.7m). The move means his stake in the Dublin-based company has increased from 26.68% to 27.94%.
Denis O'Brien, meanwhile, has been steadily increasing his stake in the company since 2006, and now holds a 22.15% stake.
The Irish billionaire, who owns mobile phone group Esat and radio group Communicorp, has argued that IN&M should sell off its loss-making UK national newspapers, the Independent and the Independent on Sunday.
IN&M's statement, published to coincide with the group's end-of-year results, marked the first time IN&M has publicly responded to O'Brien's attempts to grow his influence on the company.
Yesterday, the company said: "Since prematurely disclosing his initial investment in INM in 2006, Mr O'Brien has made a series of personalised, misleading and inaccurate attacks on the company, its board, management, strategy and governance."
O'Brien promptly responded, describing the statement as a "highly personal and unwarranted attack on the company's largest independent shareholder".
In its results yesterday, IN&M announced a 7.7% rise in pre-tax profits to €286m. UK revenue, which includes the Independent titles and the Belfast Telegraph, increased 18.3% to €268.1m.
Shares in IN&M closed last night up 8.7% at €1.87, giving the publisher a market capitalisation of around €1.45bn.