O'Brien had put forward the resolutions to remove Brian Hillery as chairman of the company and Baroness Jay as senior independent director.
The INM board said that it was "wholly satisfied" with Hillery and proposed that the resolution be dismissed at an Extraordinary General Meeting on 3 November.
RiskMetrics Group, an independent proxy advisory firm, agreed that shareholders should vote against the two resolutions.
Already in the past month, O'Brien's proposals have been defeated when the future of The Independent, which he wanted to either close or sell off, was secured.