Authorities in Mexico have arrested suspects in the killing of a seven-year-old girl whose murder rocked the capital with protests, Mexico City Mayor Claudia Sheinbaum said.

The body of Fatima Cecilia Aldrighetti was discovered over the weekend in a plastic rubbish bag, sparking outrage over growing violence against women in Mexico.

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"The alleged perpetrators of the femicide of the minor Fatima Cecilia were arrested in a town in the state of Mexico," Sheinbaum said Wednesday on Twitter.

Sheinbaum had earlier said that the two suspects are apparently a couple and that witnesses told investigators the pair had abandoned their rented home in a southern neighbourhood of the capital on Saturday, the day before the girl’s body was discovered.

Authorities searched the house on Tuesday night and found clothing and other items belonging to the girl.

Sheinbaum also said the woman was known to the girl's family. The previous day, Aldrighetti's grandfather told The Associated Press news agency that he did not recognise a police sketch of the female suspect, but authorities on Wednesday released photographs of both suspects.

Aldrighetti, who was buried on Tuesday by grieving family members, friends and neighbours, was seen on surveillance video leaving her school on February 11 with a woman who was not her mother. That day her mother was about 15 to 20 minutes late in picking her up, according to family members.

The killing sparked outrage over growing violence against women in Mexico [Edgard Garrido/Reuters]

In Mexico City, grade-school students often walk out of school after classes to meet parents waiting on the sidewalks, but there have been few controls to ensure someone is there to meet them.

The girl's grandfather and others have criticised the school for turning Aldrighetti out onto the street when classes were done for the day and for not calling police to come get her when there was no parent present to pick her out.

Children who are not picked up are supposed to be taken to a prosecutor's facility in the central neighbourhood of Doctores. It can take an hour or more to get there from outlying neighbourhoods, especially when the sprawling capital's notorious traffic is at its peak.

Outrage over recent killings

With the death of Aldrighetti, officials have said they plan to have prosecutor's offices around the city care for children who are not picked up until their parents are able to claim them.

Sheinbam said officials also plan to bolster protocols for identifying people who pick kids up from school, accelerate deployment of security cameras and have uniformed workers on hand for security at drop-off and pick-up hours.

City prosecutors said the arrest warrants would be on charges of kidnapping with intent to cause harm. More charges such as for murder could be added later.

Authorities lost a full day in searching for Aldrighetti because they waited for a formal missing person's case file to be opened.

Sheinbaum said officials were reviewing the timeline of response from when the girl was first reported missing.

The abduction and killing of the seven-year-old came just two days after Ingrid Escamilla, a young Mexico City resident, was allegedly murdered by a boyfriend. The man, who has been arrested and purportedly confessed to killing Escamilla with a knife, mutilated her body and flushed part of her corpse into the sewer.

Outrage grew after local media published horrific photos of the skinned corpse, apparently leaked by city police officers.

The killings have proved a politically difficult issue for President Andres Manuel Lopez Obrador, who said protests over the killings were an attempt to distract attention from his social programmes.

Last week, Lopez Obrador showed little patience for those who questioned him about the government's commitment to fighting violence against women.

"This issue has been manipulated a lot in the media," the president said on Monday, adding, "I don't want the issue just to be women's killings."

In the wake of the protests, Mexico's lower house of congress has proposed toughening prison sentences for the murder of women and sexual abuse of minors.