A shooting at a school in Minneapolis that left two children dead and 17 others injured is being investigated as an anti-Catholic hate crime, the FBI says.

"The FBI is investigating this shooting as an act of domestic terrorism and hate crime targeting Catholics," FBI Director Kash Patel said in a post on X.

The two children, aged eight and 10, were killed when an attacker opened fire through the windows of the city's Annunciation Church on Wednesday morning as children were celebrating Mass.

The attacker, who died at the scene of a self-inflicted gunshot wound, was later named by police as 23-year-old Robin Westman.

Authorities have not yet released a suspected motive for the attack.

A constant stream of mourners arrived at the scene on Wednesday night, some leaving flowers.

There was a sense of shock and anger that this had happened at the start of a church Mass ushering in the new school term.

Pope Leo XIV, the first American pope, was among those who paid tribute to the young victims, saying he was "profoundly saddened" by the attack.

Police Chief Brian O'Hara told reporters: "This was a deliberate act of violence against innocent children and other people worshipping."

"The sheer cruelty and cowardice of firing into a church full of children is absolutely incomprehensible," he said.

Police began receiving calls of a shooting just before 08:00 local time (13:00 GMT) on Wednesday.

The attacker approached the side of the church, which also houses a school, and fired dozens of shots through the windows using three firearms - a rifle, a shotgun and a pistol. Police also found a smoke bomb at the scene.

Officials are investigating if the suspect shot inside the building or if all the shots came from outside the church, noting that no casings from bullets were found inside.

One neighbour, Patrick Scallen, told the BBC he ran towards the shooting after hearing the gunfire and saw three children fleeing the church, one of them a girl with a head wound.

"She kept saying 'Please hold my hand, don't leave me' and I said I wasn't going anywhere."

A 10-year-old boy who survived the attack told CBS affiliate WCCO that his friend saved him from bullets by lying on top of him.

"I was like two seats away from the stained glass window," he said. "My friend, Victor, saved me though, because he laid on top of me, but he got hit."

"My friend got hit in the back, he went to the hospital... I was super scared for him but I think now he's okay," he said.

The Annunciation Church, located in a residential area of southern Minneapolis, teaches students aged between 5 and 14.

The attacker's mother, Mary Grace Westman, previously worked at the school, according to a school newsletter from 2016. A post on Facebook says she retired from the role in 2021.

Police found a note that Westman scheduled to publish online at the time of the shooting. Investigators have since deleted the post.

Westman's name was legally changed from Robert to Robin in 2020, Minnesota court records show. In the application the judge wrote: "Minor child identifies as a female and wants her name to reflect that identification."

Speaking at a press conference on Wednesday, Minneapolis Mayor Jacob Frey pushed back against hatred directed towards the transgender community in the wake of the attack.

In their own updates, Homeland Security Secretary Kristi Noem said Westman was a "man, claiming to be transgender", and in his post on X, Patel referred to Westman as "a male".

Minnesota Governor Tim Walz said President Donald Trump and his team had expressed their "deep condolences" and offered assistance.

He said the situation was "all too common - not just in Minnesota, but across the country", adding that he hoped no community or school ever had to go through a day like this.

Trump later said the US flag would be flown at half-mast at the White House as a show of respect to the victims.