In early November, Broadcom, a key Apple supplier, offered $70 per share for Qualcomm, which the board rejected as too low. Tan then nominated alternative candidates to replace all 11 members of Qualcomm's board of directors in a hostile takeover bid.
Qualcomm shareholders are scheduled to vote on either Broadcom's or Qualcomm's board candidates by the company's annual meeting on March 6.
Tan turned up the pressure on Monday by boosting his offer to $82 per share -- with $60 in cash and $22 in Broadcom stock.
The new price values Qualcomm at $121 billion, making the proposed merger the largest ever in tech. It would create a semiconductor juggernaut that would trail only Intel and Samsung in revenue. It also would have leading market position in nearly all of the high-value chips used in smartphones.
In the letter Thursday rejecting the new offer, Qualcomm's board wanted to know if Tan was willing to pay more.
"You proposal ascribes no value to our accretive NXP acquisition, no value for the expected resolution of our current licensing disputes and no value for the significant opportunity in 5G," wrote Jacobs.
Re of Fairbanks Capital said Qualcomm "made it pretty plain in the letter that if there is not a higher price coming, they are not interested."
Qualcomm also contends the huge deal would get heavy scrutiny by global competition regulators, who could block it.
During a long regulatory probe, Qualcomm customers, particularly those in China that have already expressed concerns about Broadcom raising prices, could begin designing Qualcomm chips out of their devices.
In addition, more device makers could join Apple and another company -- believed to be Huawei -- who have stopped paying patent royalties to Qualcomm.