The activist investor targeting U.S. railroad operator CSX Corp. (CSX.O) said in a letter to the company's board on Thursday that he was willing to adjust certain demands as long as his CEO candidate was guaranteed a four-year contract.

The letter from Mantle Ridge LP's chief executive officer, Paul Hilal, to CSX's board is the latest development in the leadership fight brewing over the $10 billion rail company.

Mantle Ridge, which said it owns about 4.9 percent of CSX stock, is trying to install railroad veteran Hunter Harrison as CSX's chief executive. Harrison is the ex-CEO of Canadian Pacific Railway Ltd and a turnaround expert highly respected across the industry.

CSX's shares have risen by more than 30 percent since Jan. 18, when news of Hilal's plan to make Harrison the company's CEO broke, following a release announcing Harrison's early departure from Canadian Pacific.

The letter from Mantle Ridge, Hilal's newly launched fund after leaving activist firm Pershing Square Capital Management, comes two days after CSX called for a special meeting of its shareholders to vote on the demands Hilal has laid out in private negotiations.

CSX on Tuesday said Harrison's proposed pay package was estimated to be $300 million and said Mantle Ridge was seeking substantial representation on the company's board.

Mantle Ridge said on Thursday that it was only seeking director seats for Hilal and Harrison and that the other four director candidates were independent professionals from a list that CSXboard member Edward Kelly had vetted.

Hilal said in the letter that CSX had exaggerated Harrison's compensation figure and said his chief concern was that the board was only willing to consider Harrison for a two-year deal as CEO.

CSX said in statement on Thursday that its board would review Mantle Ridge's letter.

Hilal said he was willing to drop one independent director candidate from his proposal if CSX's board could guarantee Harrison a four-year deal.

CSX said in its statement on Tuesday that it would call a special shareholder meeting on March 16 for investors to vote on Harrison's pay package and on the company's board composition.

CSX's board is made up of 12 members, which includes current CEO and Chairman Mike Ward, who has previously signaled he plans to step down.