Blavatnik's Access Industries, which already owns 42.5 percent of Perform, on Monday announced plans for a 260p per share offer, matching the price at which the company floated three years ago.
"The board values Access Industries as a long-term shareholder and supporter of the company but has concluded that the final cash offer undervalues the Company and its prospects," Perform said in a statement.
Shares on Perform traded little changed at 258.2p at 1213 GMT on Wednesday, having surged 26 percent when Access announced the approach on Monday.
There was no immediate response from Access to Perform's rebuff on Wednesday. It had said on Monday that the offer, valuing the company including its own stake at 701.6 million pounds, was a final one.
Perform buys online rights to major sports events and supplies video clips, live action and sports news and data to media groups and bookmakers.
It established a reputation as a growth stock as it doubled its market capitalisation, before crashing in December 2013 when it issued a major profit warning and saw its shares plunge more than 50 percent in one session.
Investment bank Rothschild is advising Perform while Credit Suisse is working on behalf of Access.
(Writing by Keith Weir, editing by Susan Thomas)
