AT&T customers have also reported receiving the congestion message.
Verizon is threatening to sue Netflix over a message the video site is displaying to users when their videos stall and buffer.
"The Verizon network is crowded right now," a message to one user read. "Adjusting video for smoother playback."
Verizon is furious that it is being blamed for poor video quality and is warning Netflix it could face legal action over the "false accusations."
"There is no basis for Netflix to assert that issues with respect to playback of any particular video session are attributable solely to the Verizon network," Randal Milch, Verizon's general counsel, wrote in a cease-and-desist letter Thursday to his Netflix counterpart, David Hyman.
In all likelihood, the problems are a result of how Netflix has chosen to connect its video content to Verizon's network, Milch claimed.
Instead of connecting directly to all broadband networks, Netflix sometimes relies on other companies to carry its traffic to the Internet service providers.
Blaming the Internet service providers, who only control the last mile of the network, is "self-serving, deceptive, inaccurate and an unfair business practice," Milch wrote.
He demanded that Netflix stop showing the notices and that the company provide a list of all users who have received the notices.
Joris Evers, a Netflix spokesman, said the messages are about consumers "getting what they paid for from their broadband provider."
"We are trying to provide more transparency, just like we do with the Netflix ISP Speed Index, and Verizon is trying to shut down that discussion," Evers said. The ISP Speed Index allows consumers to compare Netflix performance on various providers.
AT&T customers have also reported receiving the congestion message, but it's unclear what other providers Netflix is targeting.