(Updates with Phillips 66's comments in the last paragraph.)

Phillips 66 (PSX) shareholder Elliott Investment Management said Wednesday that findings from its third-party survey of the oil company's institutional investors showed they "share Elliott's frustration" with alleged "underperformance and lack of a compelling strategic direction."

Elliott, which holds about 6% of the oil company's shares, wants investors to vote for its slate of four directors at the Phillips 66 annual shareholder meeting on May 21.

"Elliott clearly struggles with the definitions of independent and third-party," a Phillips 66 spokesperson said in an email statement to MT Newswires. "We are confident shareholders will recognize that paid consultants are not independent investors, and Elliott's proxy solicitor is not a third-party pollster."

Phillips 66 shares rose 1.9% in after-hours trading.