O'Brien, who previously held a 22.67% stake the company, is rumoured to be planning a takeover bid of the company, which owns UK titles The Independent and The Independent on Sunday. as well newspapers in India and Ireland.
INM chief executive Anthony O'Reilly remains the group's biggest shareholder with a stake of more than 27%, having recently increased his holding.
The increase in O'Brien's stake comes ahead of the company's AGM on 11 June. If O'Brien reaches the 25% shareholding by that time he would have powers to call an EGM (emergency general meeting) and block key company decisions at the AGM.
O'Brien, who has been deemed a dissident shareholder by the INM board, has in the past called for the group to sell off its two loss-making UK newspapers.
United Kingdom
O'Brien nears key Independent News and Media stake
LONDON - Irish tycoon Denis O'Brien has increased his stake in Independent News & Media (INM) for the second time in two days, to 23.61%, edging him closer to the 25% threshold that would hand him a major say in the running of the company.