3PAR said on Thursday that HP's $33-a-share offer was superior to Dell's latest $32-a-share offer.
It said it intends to terminate its previous merger agreement with Dell, although it was technically still in effect. Dell could come back with another offer.
3PAR shares rose $1.55, or 4.8 percent, to $33.63 in early trade. They had mostly traded around $10 this year, until Dell announced its $18 per share bid in August.
Analysts have said HP, with $115 billion in annual revenue compared with Dell's $53 billion, was likely to outbid Dell. HP also has a bigger and more global sales force that could help 3PAR grow faster.
But Dell has also shown persistence, and many had not expected it to bid to such high levels.
HP's latest offer values 3PAR at over eight times sales, and many analysts have said that was too high for a company that has barely made a profit since it was founded in 1999. Multiples above five are considered lofty in technology deals.
Others, however, say 3PAR is worth it. The company specializes in data storage, considered a key part of cloud computing -- an increasingly popular technology that enables computer users to access data and software over the Internet, allowing companies to cut costs.
Bidding wars are rare in the tight-knit technology sector. In the last notable bidding war in the tech industry, EMC Corp
Credit Suisse Group AG
(Reporting by Ritsuko Ando, editing by Gerald E. McCormick and Ilaina Jonas)