(Reuters) - Billionaire investor Carl Icahn cut his stake in rig provider Transocean Ltd by more than two-thirds "for tax planning purposes."

The move comes a week after the activist investor trimmed his stake in U.S. natural gas producer Chesapeake Energy Corp, indicating that he was reducing his exposure to oil-exposed companies.

Icahn, who accumulated a nearly 6 percent stake in Transocean in November 2013, reduced it to 1.5 percent, according to a regulatory filing on Wednesday. (http://bit.ly/2cWEzvf)

Icahn said his director designees would continue to serve on Transocean's board on the company's request.

Chesapeake said on Tuesday that two directors, including a representative of Icahn, resigned from its board.

Transocean's shares were down 0.99 percent at $9.92 in after-market trading on Wednesday.

(Reporting by Anet Josline Pinto in Bengaluru; Editing by Sriraj Kalluvila)