Sao Paulo state governor João Doria said after visiting the school: "It's a very sad scene, the saddest thing I've seen in my entire life".
Doria said the school had been evacuated and police were inspecting possible explosives left by the shooters.
Police are seen at the Raul Brasil School after a shooting in Suzano, Sao Paulo state, Brazil, March 13, 2019.
Monteiro opened fire with a.38 calibre handgun and de Castro used a crossbow, de Campos said, adding that forensics would determine how the victims died.
After shooting at students in the yard, the attackers headed to the language centre where several pupils were hiding and "committed suicide in a corridor", Sales said. Nine others were wounded in the school attack and hospitalized, he said.
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"My friend was stabbed in the shoulder and my other friend was shot", she said. "It didn't take long until police arrived".
Latin America's most populous nation has the largest number of annual homicides in the world, but school shootings are rare.
However, current Brazilian President Jair Bolsonaro signed a temporary decree in January that made it easier for citizens to buy guns in an effort to overturn the strict regulations of the past.
The last major school shooting in Brazil occurred in 2011, when 12 students in Rio de Janeiro were shot dead by a gunman. Soon after being inaugurated January 1, Bolsonaro issued a decree making it easier for people wanting a gun to buy and possess one.
The Raul Brasil Professor public school has more than 1,600 students from elementary to high school grades, teachers gathered outside said.