O'Brien now holds around 188.4m ordinary shares, which is an increase of 1.6% from his former holding of 21.07%.
Earlier this month, Sir Anthony O'Reilly, chief executive of INM, increased his stake to 27.88%, up from 26.63%.
Both men's shareholdings were diluted at the end of March when INM completed an all-share deal to acquire the remaining 50% stake in African outdoor advertising company Clear Channel Independent.
O'Brien, who has been labelled a dissident shareholder by the INM board, could call emergency meetings and block resolutions if he takes his stake up to 25%.
He has been calling for INM to sell off its loss-making flagship titles, The Independent and Independent on Sunday.
The media group, which also has investments in South Africa and Australia, is due to hold its annual meeting on June 11.
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