The offer equates to $8.8 billion for the firm or $63 a share, $2 below UnionBanCal's closing price yesterday.
Mitsubishi, which already owns 65 per cent of the San Francisco-based firm, unveiled the bid to take total control Tuesday.
UnionBanCal board member Richard Farman said: "The proposed price does not reflect the strength of UnionBanCal's strong capital position, the superior credit quality of its assets, and its potential for profitable asset and core deposit growth in the current market environment.
"The special committee believes any valuation of UnionBanCal should not be inappropriately impacted by these negative factors, and the operating challenges facing many industry participants are creating opportunities for UnionBanCal."
Mitsubishi spokesman Takashi Takeuchi indicated that the Japanese bank was still willing to "engage with discussions" with UnionBanCal over the bid.
"There is no change in our position regarding our willingness to have discussions with the special committee," he added.