Cisco is suing Apple Computer for trademark infringement in a US federal court, for using the iPhone name.
Apple launched its new handheld device under the iPhone name on Tuesday, at the Macworld event in San Francisco.
Following the launch Cisco said it hoped to resolve the matter by Tuesday evening after negotiations.
Apple responded by saying the lawsuit was "silly" and that Cisco's trademark registration was "tenuous at best".
"We think Cisco's trademark lawsuit is silly," Apple spokesman Alan Hely said. "There are already several companies using the name iPhone for Voice Over Internet Protocol (VOIP) products."
"We are the first company to ever use the iPhone name for a cell phone, and if Cisco wants to challenge us on it we are very confident we will prevail."