Chesapeake's board is under increasing fire from investors who want to see tougher oversight of Chief Executive Officer Aubrey McClendon. The company, in the midst of governance crisis, is also struggling financially as low natural gas prices take a toll.

In a letter on Tuesday, New York State Comptroller Thomas DiNapoli said withholding votes from board members V. Burns Hargis and Richard K. Davidson was a "necessary first step toward reconstituting a board that is currently entrenched and unaccountable to shareholders."

On Friday, activist investor Carl Icahn disclosed that he had taken a 7.6 percent stake in Chesapeake and called on the company to replace at least four directors.

Icahn asked the company for two board seats for his own representatives and two for another large shareholder such as Chesapeake's largest, Southeastern Asset Management.

Icahn's investment "will put increased scrutiny on both the board and management's activities, as he specifically criticized the board with respect to corporate governance ...," analysts at Simmons & Co told clients on Tuesday.

Shares of Chesapeake rose nearly 6 percent, bolstered by news of Icahn's stake.

DiNapoli said Hargis, who has been on the board since 2008, and Davidson, a director since 2006, are both on the audit committee, which has failed to monitor McClendon's mortgages on his stakes in company wells.

"In my view, there needs to be an evaluation of the entire board's competence and performance, including an assessment of whether the current directors have the necessary skills and attributes to continue to oversee the company," DiNapoli said in the letter.

A spokesman for the company dismissed DiNapoli's call for board changes as "old news."

On April 18, Reuters reported that McClendon had taken out more than $1 billion in personal loans, using his interest in thousands of company wells a collateral. McClendon's lender, EIG Global Energy Partners, is also a big investor in Chesapeake, a situation that may put the executive's interest at odds with shareholders.

Earlier this month, New York City Comptroller John Liu urged shareholders to withhold support for Davidson, a former CEO of Union Pacific Corp., and Hargis, who is president of Oklahoma State University.

Chesapeake's shareholder meeting is scheduled for June 8.

The company's shares were up 5.8 percent at $16.72 in late morning New York Stock Exchange trading.