A new statement shared by Erik's wife Tammi on Friday said the family had been "victimized" by what they called "a grotesque shockadrama".

The group of 24 family members, spearheaded by the brothers' aunt, said they wanted the brothers "home with us," and believed the show to be "riddled with mistruths and outright falsehoods".

They said no one from the show had ever directly spoken to them and suggested Monster was in fact "all about" Murphy himself.

Speaking to Variety, Murphy - creator of the equally controversial Monster: The Jeffrey Dahmer Story - said the family's response was "predictable at best".

He called on the family to specify what it was in the show they believed amounted to "lies after lies".

Lyle and Erik Menendez were convicted of shooting their father and mother Jose and Mary Louise "Kitty" Menendez multiple times at close range in the family mansion in Beverly Hills, California, on 20 August 1989. They were 21 and 18 at the time.

During their trial, the defence claimed the brothers committed the murders in self-defence after many years of alleged physical, emotional and sexual abuse.

Read more:
What was the Menendez brothers murder case?
Monsters star supports Menendez brothers in call for retrial
Kim Kardashian visits Menendez brothers

The prosecution argued the murders were motivated by greed, and said the brothers killed their parents to avoid disinheritance.

Murphy's drama explores the killings as well as the trials that followed, resulting in the brothers' conviction for life without possibility of parole in 1996. Murphy has previously said the drama portrays both the parents' and the brothers' side of the story.

Speaking to Variety, Murphy said his show meant the brothers "are now being talked about by millions of people all over the world… giving these brothers another trial in the court of public opinion".

He said he believed "it's really opened up the possibility that this evidence that they claim that they have, maybe that there is going to be a way forward for them".

The Menendez brothers' defence team say they have two new pieces of evidence which were not available when the case was first presented to a jury and are hoping to secure a retrial.

Murphy said he believes that if the trial was held today - when male sexual abuse is better understood - the brothers would be given a lesser charge and lighter sentence.

He said that while he "wished them well," he had "no interest" in talking to the brothers.

Earlier this week, Monsters actor Cooper Koch told Sky News he had recently met with the brothers at San Diego County's Richard J Donovan Correctional Facility along with Kim Kardashian.

Koch, who plays Erik Menendez, said he backed calls for a retrial, adding: "I totally stand with them, and I support them, and I can only hope that the justice system makes the right decision".

He said visiting the brothers had been "a very rewarding experience," and had changed his life.

Responding to Erik Menendez's criticism of the show as "dishonest," Koch told Sky News: "I understand where he's coming from.

"It's very difficult to have your life dramatised and retold in a Hollywood retelling of the biggest trauma of your life. One that has, in a sense, defined you.

"I can only sympathise and empathise with him and stand with him. You know, I get it."

Next month, Netflix will release a documentary about the Menendez case, featuring extensive audio interviews with Lyle and Erik, as well as lawyers involved in the trial, journalists who covered it, jurors, and family members - seemingly with the brothers' full approval.