"The issue that we have with Qualcomm is that they have a policy of no license, no chips. This is, in our view, illegal," Cook said on "Mad Money."
"And then, secondly, they have an obligation to offer their patent portfolio on a fair, reasonable, and non-discriminatory basis and they don't do that. They charge exorbitant prices."
The companies have been locked in lawsuits for years. Apple has accused Qualcomm of unfair patent licensing practices. Qualcomm has in turn accused Apple of patent infringement, and has filed injunctions in China and Germany to halt iPhone sales.
Cook also took issue with marketing tactics supposedly employed by Qualcomm. The New York Times reported in November that Qualcomm hired Definers Public Affairs to write and spread false stories about Apple to confuse national story lines.
"The paying somebody to write fake news and then promoting it: This is stuff that should be beneath companies. This is not how things should operate," Cook said.
"We haven't been in any settlement discussions with them since the third calendar quarter of last year," Cook said Tuesday. "So I'm not sure where that thinking is coming from."
Responding to Cook's comments, a Qualcomm spokesperson said they were "once again misleading and appear to be a deliberately timed attempt to tarnish our company's reputation."
"We have been consistent for the last eighteen months in making clear that we have, at various times, been in discussions with Apple about a possible resolution to our licensing dispute," Qualcomm said in a statement.
—Reuters contributed to this report.