Vivendi has raised its stake in French publishing group Lagardere to 21.19%, becoming its largest shareholder, and could ask for one or more seats on its supervisory board, stock market watchdog AMF said on Wednesday.

Vivendi, which also now controls 16.01% of Lagardere's voting rights, said it could buy more Lagardere shares, market conditions permitting, but would not seek control of the company, the regulatory filing showed.

Lagardere has been locked in a battle with London-based hedge fund Amber Capital for four years. Lagardere shareholders in May rejected calls from the the activist investor, which has a stake of about 18%, to replace Lagardere's supervisory board.

In May, France's business elite closed ranks around Lagardere in its fight against Amber.

Vincent Bollore's Vivendi increased its stake in Lagardere to 16.48% at that time, while LVMH's Bernard Arnault, bought a 25% stake in Lagardere Capital & Management (LCM), the holding company of Lagarere boss Arnaud Lagardere.

(Reporting by Dominique Vidalon; Editing by Mark Potter)