Police said the two children were believed to have been caught in the gunfire unintentionally as bystanders to Monday's violence, which unfolded several miles from the scene of a December 2015 shooting rampage that killed 14 people.
San Bernardino Police Chief Jarrod Burguan said the shooting at North Park Elementary School in San Bernardino, about 65 miles east of Los Angeles, was an apparent murder-suicide.
Investigators worked to confirm the identities of the gunman and the dead woman to determine their relationship, if any, and whether the shooting stemmed from a domestic dispute, police Captain Ron Maas said at a news conference.
The wounded students were hospitalised but their medical conditions were not immediately known. Maas said they were not related to either of the dead adults.

Students from North Park Elementary School in San Bernardino, Calif., line the fence (AAP) Source: AAP
School district secretary Vicki Wood confirmed the dead woman was the teacher and that she was teaching a special-education class at the time. Police said she and the gunman were the only adults in the classroom.
Authorities provided few details about the circumstances of the shooting, except to say that the gunman had gained entry to the school as a visitor and kept his weapon concealed until he opened fire inside the classroom.
The school was evacuated and students were bused to the campus of California State University at San Bernardino to be briefed and interviewed by authorities. From there, they were to be taken to a nearby high school to be reunited with their families, police said.
Aerial television footage from the scene showed children holding hands and walking single-file across the campus from the school building to waiting buses.
One young student, reunited with her mother, told local NBC News affiliate KNBC-TV that the incident left her "super scared." Anxious parents interviewed on camera said they had been given no information from the school other than where their children were being taken.

Parents and family of North Park Elementary School students stand across the street from the school waiting to hear from their children (AAP) Source: AAP
School officials said North Park Elementary would remain closed for at least two days.
The city of San Bernardino last made national headlines on Dec. 2, 2015, when a husband and wife who authorities said were inspired by Islamic extremism opened fire on a holiday office party of county health workers, killing 14 people and wounding more than 20. The couple, Syed Rizwan Farook and Tashfeen Malik were killed by police during a shootout.
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