Anderson and Smith were found dead in a special needs classroom that serves the first through fourth grades, Burguan said.
San Bernardino Police Chief Jarrod Burguan says on Twitter that investigators believe "the suspect is down".
Authorities said that Anderson signed in at the school office then proceeded to the classroom.Although the shots fired were aimed at Smith, two students standing her were struck by the gunshots before Anderson turned the gun on himself.
The other student shot, only identified as a 9-year-old boy, was in stable condition Monday afternoon.
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But South Korea and the U.S. say the sole goal of the THAAD system is to guard against potential missile threats from North Korea. It was also the first visit to South Korea by a senior Chinese official since the planned deployment of the U.S.
"We believe this to be a murder-suicide", San Bernardino Police Chief Jarrod Burguan tweeted.
"I see one of my boys, but not the smallest one", he said tearfully. "They know exactly what to do and what they need to do to keep students safe", Said Garcia to KTLA. "The victim was his wife the teacher, Karen Elaine Anderson, 53". "The children we do not believe were targeted", said police Capt.
Frantic parents running up a sidewalk looking for information about their children were not able to learn immediately what happened.
One of two students injured in the murder-suicide later died at a hospital, Burguan said.
Mayor Carey Davis said he had spoken about the shooting to White House officials about Tuesday's (AEDT) school shooting.
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President Donald Trump, before his election, described fighting ISIS and seeking Assad's removal at the same time as "idiocy". It is easy to see why this decision was necessary, but we are right to wonder what will happen in the coming days.
Monday's shooting was the latest tragedy for a city that has struggled in recent years with more than its share of them.
Authorities locked down the school - which will be closed for at least two days - and students were safely escorted to Cal State University where they united with parents, reports ABC7. Aerial television footage from the scene showed students walking single-file across the campus from the school building.
"This is a tragic incident that has befallen our city", San Bernardino Police Lt. Michael Madden told reporters earlier.
An eight-year-old boy died when a gunman opened fire in a San Bernardino elementary school Monday morning.
Marina Ramos told KABC that she rushed to the school to try to pick up her grandson.
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Troy Daniels caught fire in the fourth quarter from three, and he had 8 points on the night in 14 minutes of play. We'd rather it be him [getting the rebound]", Steven Adams told ESPN's Royce Young in December.
The elementary school is located at 5378 N. H St.