Separately, Considine said investigators had determined that the rear school door through which the gunman entered had been closed by a teacher before the shooter arrived but had failed to lock behind her - contrary to a DPS account last week that a teacher had left the door propped open.
“The investigation continues into why (the door) did not lock,” Considine added.
The shooting, the deadliest at a US school since 26 people were slain at Sandy Hook Elementary School in Connecticut, came 10 days after 10 people were killed by an 18-year-old gunman at a supermarket in Buffalo, New York. The back-to-back massacres have reignited a national debate over federal and state gun laws.
Texas law allowed the Uvalde shooter to purchase an AR-15-type weapon on his 18th birthday, a week before the massacre. He also bought hundreds of rounds of ammunition and a second rifle in subsequent days.
U.S. President Joe Biden, who travelled to Uvalde on Sunday, has joined many fellow Democrats in calling for new gun restrictions, such as a ban on assault-style weapons and universal background checks for all firearms purchases.
In New York, Democratic political leaders said on Tuesday 10 bills to tighten gun laws had been introduced in the state legislature, including one to raise the minimum age for buying semi-automatic rifles to 21.
Republicans have successfully held off tougher firearms control and in many states have relaxed gun regulations in recent years, saying law-abiding citizens have a constitutional right to bear arms.
Republican Arkansas Governor Asa Hutchinson, widely seen as potential 2024 candidate for president, made headlines by saying on CNN he was open to discussing raising the minimum age to purchase a semi-automatic rifle from 18 to 21.