The moves come after two pension funds said they were against the deal, while the State Teachers Retirement System of Ohio told CNET News.com they would their 3.5 million HP shares and 4.3 million Compaq shares in favor of the deal.
Intel's move is almost entirely symbolic. An Intel representative said the company would vote the 58,836 shares it directly controls in favor of the deal. Another 525,440 shares are owned as part of a profit-sharing program for Intel employees, but the company does not decide how those shares will be voted.
Banc One owned 5.1 million HP shares as of Dec. 31, according to an HP press release.
The moves by Intel and Banc One come as HP is trying to line up support ahead of Tuesday's.
The proposed, which is valued at more than $21 billion, is being opposed by board member and Hewlett heir Walter Hewlett, as well as Hewlett and Packard family members and institutions representing 18 percent of HP shares. Other institutions representing about 3 percent of HP shares have come out against the deal, while those representing about 8 percent of shares have come out in favor.
HP and Compaq are two of Intel's largest customers and the combined company would clearly be even more important. HP is seen as the more independent of the two companies and less likely to directly follow Intel's product plans.
On Wednesday, HP Labs Director Dick LampmanHP has no intention of handing over its server architecture to Intel in a post-merger world.