TOKYO (Reuters) - Influential proxy advisory firm ISS recommended shareholders against reelecting Takata Corp Chief Executive Shigehisa Takada to the company's board of directors, saying he should be held responsible for its defective air bags.

Takata is seeking financial support as it faces mounting liabilities related to a massive global recall of its potentially faulty air bag inflators. It is due to hold its annual shareholders' meeting on June 28.

Fifty-year-old Takada, the grandson of the company's founder, has been widely criticised for keeping a low profile even as the air bag crisis escalated. Takada has offered to resign once an agreement is reached over a financial rescue for the company, a source recently told Reuters.

ISS also recommended shareholders push out Toshiba Corp Chief Executive Satoshi Tsunakawa, saying he allowed former executives to retain influence despite the company's pledge to improve governance in the wake of a multi-billion dollar accounting scandal.

Former president Taizo Nishimuro was named honorary advisor earlier this year, a move ISS said signaled Toshiba was not determined to change its corporate culture, which was blamed for widespread accounting irregularities.

"Tsunakawa should be held responsible for the company's continued practice of allowing its former executives to retain influence, and thus preserving its corporate culture which is a root cause of the highly-publicised accounting fraud, instead of breaking away from it," ISS said in a report.

Proxy advisors such ISS and Glass, Lewis & Co have gained influence in Japan in the past year due to the adoption of a new shareholder code, which calls on institutional shareholders to disclose how they vote, part of a government drive to improve corporate governance.

(Reporting by Ritsuko Ando)