After leading a prayer group, Marie Cabrera, right, embraces one of the group members near a sidewalk memorial dedicated to the teacher and student who were shot to death Monday at North Park Elementary School in San Bernardino, Calif., Tuesday, April 11, 2017.

San Bernardino police have said nothing of what might have motivated Anderson to open fire in the special education classroom at North Park Elementary School on Monday.

Children with the syndrome can have learning disabilities and heart problems akin to hardening of the arteries, frequently requiring surgery.

Another child caught in the crossfire was rushed to a hospital and said to be in critical condition."This does appear to have been a murder-suicide with both male adult and female adult victim succumbing to injuries, with the male succumbing to a self-inflicted gunshot wound", Lieutenant Mike Madden of the San Bernardino Police Department told a news conference on Monday.

Anderson had told school personnel he was there to drop something off to his wife, which is "not uncommon", according to Burguan.

While San Bernardino has long struggled with high levels of violence, last year it marked a grim milestone as police recorded 62 killings - making it the deadliest year since 1995.

Anderson was a "known person" by school staff, and all the precautionary procedures were taken to confirm his identity when he arrived at the school, San Bernardino Unified School District Superintendent Dale Marsden said.

The two students who were struck were reportedly standing behind Smith when Anderson started shooting.

Investigators found a note that made reference to the couple's relationship, feeling dishonored and "moving forward with no regrets", Burguan said.

Two male students, who were injured as Anderson fired at his wife, were taken to a hospital for treatment, police said.

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"I think this would have been just been too traumatic for him to be here", she said.

A candlelight vigil will be held at North Park at 7 p.m. today.

Anderson then turned the gun on himself. He went to her classroom and "without saying anything" shot her with a large-calibre revolver, Mr Burguan said.

Jonathan's family has asked for privacy, Marsden said, but has released photos of their son, and gave authorities permission to talk about Jonathan's condition.

She called Jonathan "precious" and "friendly", that he loved to give hugs and was "easy to love".

"It's just about unity", Arrieta said". "That just wouldn't happen", she said.

"Parents often say the joy and perspective a child with Williams syndrome brings into their lives had been unimaginable", Marsden said Tuesday, quoting from the Williams syndrome Association. I can't imagine what these families are going through and especially these kids.

"By all accounts Jonathan Martinez was a happy child", he said.

Smith and one of her students were fatally shot Monday at North Park Elementary School by Cedric Anderson, who also wounded another little boy before killing himself.

Anderson had been arrested four times from 1982 to 2013 on a weapons charge and accusations of domestic violence and theft but was never convicted in any case, authorities said.