The 18-year-old gunman carried out the killings at Robb Elementary School in the city of Uvalde.
State Senator Roland Gutierrez who has also released the higher death toll said he was briefed by state police on the fatalities.
The teen is also suspected of killing his grandmother before unleashing the school shooting rampage, three law enforcement sources confirmed to CBS News, the BBC's US partner.
The children attending the school are aged between seven and 10 years.
The suspect was armed with a handgun and an AR-15 semiautomatic rifle, two law enforcement sources have confirmed to CBS News.
He also had high-capacity ammunition magazines when he entered the school, according to the sources.
Texas Governor Greg Abbott said the suspect is dead, and it is believed that responding officers killed him.
He named the suspect as Salvador Ramos, who lived in the area.
According to Abbott, Ramos abandoned his vehicle and went into the school carrying his weapons.
"He shot and killed horrifically, incomprehensibly, 14 students and killed a teacher," Abbott said earlier at his first media briefing.
Abbott says he and his wife, Cecilia, are mourning the day's "horrific loss" and he has urged the state of Texas to come together.
He also thanked the "courageous first responders" who worked to "secure the site" of the shooting.