"We think that our full-cash offer is still superior even after Chevron raised its bid," a spokesman for China National Offshore Oil Corporation said.
The official said he only learned of Unocal accepting an improved takeover bid by Chevron of $17.1 billion via the internet.
The spokesman, quoted by Xinhua news agency, said the Chinese company was expected to give an official response soon.
Unocal, the ninth-largest US oil company, jointly announced with Chevron earlier on Wednesday their agreement on the offer, which will be submitted to a vote by Unocal shareholders on 10 August.
Unocal had already agreed to a deal with Chevron in April when it received a rival bid in June of $18.5 billion in cash by CNOOC.
But the Chinese bid touched off a firestorm of controversy among some US lawmakers and the American public and prompted calls for Congress to intervene to block the move which was seen as a threat to US national security and its strategic energy interests.
The sweetened bid by Chevron is equivalent to $63.01 per share of Unocal common stock based on the closing price of Chevron stock on Tuesday.
Chevron's previous offer was for $60.51 in cash and stock.
By contrast, CNOOC's all cash offer amounted to $67 a share.
Dealers in Hong Kong, where CNOOC is listed, said that despite the seeming setback, its stock prospects would actually improve if it withdrew from the Unocal bid.
"CNOOC's failure to take over Unocal will be a big positive for investors," said Ken Li, an analyst at China Everbright Securities.
"Its $18.5 billion offer for Unocal is already very expensive compared to less than $15 billion which I believe is a reasonable price for that US company."