The two wireless giants have squared off over a licensing agreement that was set to expire Monday. Nokia had hoped Qualcomm would accept the payment to cover fees up until June.
Qualcomm says it rejected the $20 million offer because it contained too many conditions and because it "is a fraction of the royalty to which Nokia agreed."
A week ago, when Nokia made its $20 million gesture, Qualcomm replied by seeking an arbitrated settlement to this long-running patent licensing despute.
Nokia has said it wants to pay less or nothing in fees to Qualcomm and has received an extension of the existing contract to 2008. Qualcomm collects an estimated 4.5% royalty for every phone sold that uses its patent.
Qualcomm shares rose 62 cents to $42.72, and Nokia was down 2 cents to $23.36.