MADRID, June 28 (Reuters) - Spanish defence company Indra said on Tuesday it had started to look for new independent board members to replace the seven that were ousted or quit after shareholders unexpectedly agreed last week to give the government more control.

In a filing to stock market supervisor CNMV after a board meeting on Monday, Indra said it wanted to "restore the corporate governance structure, including, among others, the appointment of an independent vice-chairman and lead independent director."

Indra, which is 25.2% owned by state holding company SEPI, removed five of its eight independent board members last Thursday after shareholders agreed to a proposal from activist fund Amber Capital to reshuffle the board. Its shares plunged 15% the next day.

Two more board members resigned since then, although one will stay and help the company pick new independent members, Indra said on Tuesday.

The government's bigger role in the company comes ahead of the rollout of a jet fighter programme, and as Spain looks to increase defence spending in the wake of Russia's invasion of Ukraine.

The four board members said in letters to the secretary general of Indra's board and submitted by the company to the CNMV, that according to accounts from Thursday's shareholder meeting, SEPI, Basque group SAPA and Amber Capital, that represented close to 38%, had voted to oust them as independent board members.

Spanish law forces shareholders that coordinate and control more than 30% of a listed company to launch a tender offer to buy all the outstanding shares of the company.

Carmen Aquerreta said that her interest had been to ensure that Indra had a majority of independent directors, "rejecting any type of action that could imply a de facto minority of truly independent directors."

Aquerreta blamed Amber Capital for requesting board changes and participating in directors' meetings after acquiring on June 16th shares representing 4.2% of Indra's capital.

Broker Renta 4 has said the board overhaul appeared to involve coordinated action, and CNMV head Rodrigo Buenaventura told a financial event in Bilbao on Tuesday it was looking into the changes, after describing them on Friday as "worrisome".

He added the supervisor would not talk about potential concerted action until a thorough analysis had been completed.

SEPI declined to comment, while SAPA and Amber were not immediately available to comment. (Reporting by Emma Pinedo Additional reporting by Jesús Aguado Editing by Mark Potter and Bernadette Baum)