The traumatised Texan town of Uvalde has begun laying to rest the 19 young children killed in an elementary school shooting that left the small, tight-knit community united in grief and anger.

The body of 10-year-old Amerie Jo Garza arrived in a silver coffin and was carried into Sacred Heart Catholic Church by six pall bearers wearing white shirts with red carnations.

Mourners, some of them wearing the purple color of Robb Elementary School across the street, gathered outside the church ahead of the funeral amid a strong police presence.

Another girl, Maite Yuleana Rodriguez, also 10, was due to be laid to rest today, with further ceremonies scheduled through the coming weeks, including of the two teachers killed.

As the community mourned, anger has seethed over the response of police, who came under intense criticism since the 24 May tragedy over why it took well over an hour to neutralise the gunman – the "wrong decision," Texas Department of Public Safety director Steven McCraw has admitted.

The great-grandfather of one of the young victims berated police near the memorial of white crosses surrounded by wreaths and bouquets of flowers.

"They could tell me 'Oh, we made a mistake. We made the wrong decision'. But my great-granddaughter is not coming back to me," said a distraught 78-year-old Ruben Mata Montemayor.

19 children and two teachers were killed in the shooting

When US President Joe Biden visited the town, about an hour's drive from the Mexico border, over the weekend, shouts of "do something!" rang out from the crowd.

The shooting - the latest in an epidemic of gun violence in the United States that came less than two weeks after 10 people died in the attack at a Buffalo grocery store by a young gunman targeting African Americans - has spurred desperate calls for gun reform.

"There's no words to describe (it)," said Esther Rubio, who traveled from nearby San Antonio to attend a wake yesterday for Amerie Jo.

Her pictures decorated the funeral home where friends and family gathered, just across the street from Robb Elementary School, where a local 18-year-old gunned down 19 children and two teachers before he was killed by police.

People arrive at Sacred Heart Catholic Church for Amerie Jo Garza's funeral service

While mass shootings draw anguished attention and spur momentary demands for change, gun regulation faces deep resistance from most Republicans and some rural-state Democrats.

Mr Biden on yesterday vowed to "continue to push" for reform, saying: "I think things have gotten so bad that everybody is getting more rational about it."

Some key politicians have also voiced cautious optimism, and a bipartisan group worked through the weekend to pursue possible areas of compromise.

They reportedly were focusing on laws to raise the age for gun purchases or to allow police to remove guns from people deemed at risk - but not on an outright ban on high-powered rifles like the weapon used in both Uvalde and Buffalo, New York.

With the country still reeling over the Uvalde massacre - the deadliest school attack since 20 children and six staff were killed in Newtown, Connecticut in 2012 - US media reported the country was hit by a dozen more mass shootings over the three-day Memorial Day weekend.

The United States generally counts mass shootings as involving four or more deaths.

At least 132 gun deaths and 329 injuries were recorded nationwide from Saturday to Monday evening, according to the Gun Violence Archive website.

Mourners in Uvalde - a mostly Latino town of 15,000 - have echoed calls for change.

"At the end of the day, if this child cannot even sip a glass of wine because he's too young, then guess what? He's too young to purchase a firearm," said Pamela Ellis, who traveled from Houston to pay her respects.

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