(Adds Netflix letter to Verizon, Verizon response)

By Lisa Richwine and Marina Lopes

LOS ANGELES/NEW YORK, June 9 (Reuters) - Netflix Inc said on Monday it will stop sending messages that blame Verizon Inc's broadband service for slow delivery of its TV shows and movies, a move that may defuse tension between the two over Internet congestion.

The messages, which appeared on screen when a video was buffering, were a "small scale test" that will end on June 16, Netflix spokesman Joris Evers said in a post on the company's blog. But he left open the option that the alerts could resume. "We will evaluate rolling it out more broadly," he said.

The notices are part of what Netflix calls a "transparency campaign" to inform customers when "their experience is degraded due to a lack of capacity at their broadband provider's network." The company also publishes a monthly index that ranks the speed of Internet service providers.

Netflix previously said the buffering messages started in mid-May and were sent to a few hundred thousand customers of Verizon and other broadband providers when streaming was slow.

Last Thursday, Verizon, which had called the notices a "PR stunt," sent Netflix a letter that demanded that the company stop the practice and threatened legal action if it failed to provide information on who received them.

Verizon argues that the messages are deceptive and that the responsibility for slow streaming falls on Netflix. Verizon said Netflix tries to save money by using middleman to distribute the content while knowing some of them have issues with congestion in some networks.

Netflix disputed that on Monday. "Netflix does not purposely select congested routes," Evers said on the blog.

Also on Monday, Netflix sent a written response to Verizon's letter, largely echoing the blog post and adding that the streaming service "will continue to work on ways to communicate network conditions to our consumers."

"Verizon's unwillingness to augment its access ports to major Internet backbone providers is squarely Verizon's fault," Netflix General Counsel David Hyman wrote.

In addition, Netflix updated its speed index, which showed Verizon's Fios service dropped in May to 10th place out of 16 Internet providers that were measured. The previous month, Fios ranked eighth.

In April, Netflix said it reluctantly signed a deal to pay fees to Verizon to bypass the middlemen and deliver content directly to the company, ensuring faster speeds. Verizon is still implementing the needed architecture and expects to finish by the end of 2014.