The message, which appeared on Twitter earlier this week, told users waiting for their video to load that congestion with their ISP was affecting the service quality.
"The Verizon network is crowded right now. Adjusting video for smoother playback..." said a message from Yuri Victor.
The telecom firm sent a letter demanding that the video streaming service stop sending messages to customers.
"There is no basis to assert that issues with respect to playback of any particular video session are attributable solely to the Verizon network," wrote Verizon general counsel Randal Milch to Netflix's chief lawyer, David Hyman.
"Verizon demands that Netflix immediately cease and desist from providing any such further 'notices' to users of the Verizon network."
In response to the letter, Joris Evers, a Netflix spokesman, tweeted: "This is about people not getting what they paid for from their Internet service providers. Netflix is transparent, (Verizon) is shutting that down."
In a blog post on Wednesday, Verizon's VP for federal regulatory affairs, David Young, said the low quality video streams faced by Netflix customers mostly likely came from the connection that Netflix has chosen to reach Verizon's network.
The row comes after Verizon and Netflix agreed in April that Neflix could pay Verizon to connect directly to its network.