Bollore refused to rule out calling for an extraordinary general meeting if Aegis refused to vote in two of his associates as directors despite his 29 per cent stake.
Aegis, whose operating companies include Carat and Vizeum, claims this would give Havas access to commercially sensitive information about a major rival.
Lord Sharman, the Aegis chairman, told the company's annual meeting on Wednesday: "The board takes the view that there is a fundamental, irreconcilable conflict of interest."
Bollore warned the longer the dispute went on, the more likely it was that Aegis' client relationships would be damaged.
He told the meeting: "Not being represented on the board now means we can never be represented by anyone. We don't believe that's normal and we cannot accept it."
Comment, page 52.