"It is the board's unanimous belief that Broadcom's proposal significantly undervalues Qualcomm relative to the company's leadership position in mobile technology and our future growth prospects", said Paul Jacobs, Executive chairman and chairman of the Qualcomm board.
If completed at the current price, the combined companies would have had annual sales of $51 billion - trailing only Intel and Samsung in the semiconductor industry.
Qualcomm rejected Broadcom's $105 billion acquisition offer on Monday, but the battle has just begun.
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The offer also comes at a time when Qualcomm is trying to close its pending US$38-billion acquisition of automotive chipmaker NXP Semiconductors NV.
Broadcom CEO Hock Tan, who said earlier this month he would redomicile his company to the United States from Singapore, has stated he is open to launching a takeover battle.
Overall, Broadcom's bid is a very ambitious attempt to grow its share of the market for components that go into mobile phones. Apparently, it is considering raising its bid, but also wants to submit its own selection of directors for Qualcomm's board.
Qualcomm no longer has a poison pill- a tactic to make shares of the company's stock look unattractive or less desirable to the acquiring firm - in its bylaws to deter potential suitors.