Xerox said Monday it was raising its offer for computer and printer maker HP to some $36 billion as part of an effort to win over shareholders amid a heightened battle for control of the Silicon Valley firm.

The new offer from the imaging and copying giant is around 10 percent higher than the bid launched last year and rejected by the HP board of directors.

Xerox said in a statement it already has support from some large HP shareholders who "want the enhanced returns, improved growth prospects and best-in-class human capital that will result from a combination of Xerox and HP."