(Adds comments from murdered girl's grandfather, retired teacher)

By Noe Torres and Anthony Esposito

MEXICO CITY, Feb 17 (Reuters) - Mexico's President Andres Manuel Lopez Obrador on Monday appeared to blame the murder of a seven-year-old girl on the neoliberal economic model, angering critics who say the government has failed to stem a wave of gender violence.

Lopez Obrador was asked at his regular news conference about the kidnapping and killing of the girl, Fatima Cecilia Aldrighett, who went missing on Feb. 11 and whose body was discovered over the weekend inside a plastic garbage bag in Mexico City's Tlahuac neighborhood.

In response, the president said he was sure authorities would catch the perpetrators of the crime, but said punishment alone was not the solution.

The bigger challenge, he said, was to purify Mexican society, which he said had "fallen into decline, a progressive degradation that has to do with the neoliberal model."

"Unemployment, economic growth, the number of homicides are measured, but the degree of social decomposition produced by neoliberal policies is not measured. There is a deep crisis of loss of values."

Family members and parents gathered in protest on Monday outside Aldrighett's home and her school, where she was seen leaving accompanied by an adult woman last week. #JuticiaParaFatima, or Justice for Fatima, was tweeted 127,000 times and her name was a top global trend.

The girl's grandfather Guillermo Anton Godinez, standing outside the family's modest home, tears streaming down his face, said that "perhaps" Lopez Obrador is right that the economic model is partly to blame. "But now he is in charge, he is president ... He should show us he is different from past administrations."

Lopez Obrador regularly blames Mexico's most salient problems, such as corruption, poverty and violence, on the policies implemented during the era of pro-market policies such as economic liberalization starting in the 1980s.

"That's why we voted for this president, but what has the president done. He's all talk ... This hurts us. We want justice," retired teacher Josefina Meza said outside the girl's school.

The murder of the girl comes after demonstrators on Friday daubed the words "femicide state" in blood-red on the door of Mexico's National Palace and demanded justice for 25-year-old Ingrid Escamilla, who was brutally murdered last week.

Lopez Obrador on Monday publicly asked the feminist protesters not to paint the walls and door of the palace, saying his government was working to end the murder of women.

In a news conference, the attorney general's office confirmed Aldrighett's body had been identified and offered a 2 million peso ($107,000) reward for information leading to those responsible for the murder.

An average of 10 women a day are killed in Mexico and 2019, the first year of Lopez Obrador's government, marked a new overall homicide record, official data shows. Victims of femicide increased 10% in 2019 to over 1,000.

The World Health Organization says femicide is generally understood to involve the intentional murder of women because they are women, but broader definitions include any killings of women or girls.

"It is not the fault of the neoliberal model. It is not the fault of poverty. Dehumanization is at fault and your comments do not help," Twitter user @VMOSN said, responding to Lopez Obrador.

Others on social media pointed out that other countries in the world that have free-market economies do not suffer the levels of gender violence seen in Mexico.

($1 = 18.5682 Mexican pesos) (Reporting by Noe Torres, Anthony Esposito and Raul Cortes Fernandez; Editing by Marguerita Choy and Andrea Ricci)

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