Dewhurst, a Republican, said school districts would nominate who they wanted to carry weapons on campus. The training would be more extensive than what is currently required for a Texas concealed handgun license and include how to react in an active shooter situation.
"God forbid we should have an active shooter crisis in our schools," Dewhurst said.
His proposal came in the aftermath of last month's mass shooting at an elementary school in Newtown, Conn., where a gunman slaughtered 20 children and six adults before killing himself. Vice President Joe Biden has been meeting with groups this week to develop policy recommendations on how to prevent such tragedies.
The National Rifle Association has called for armed guards in every school in America and rejected any further restrictions on gun purchases or ownership.
Dewhurst said the eight hours of class instruction and two hours of shooting training for a concealed handgun license is "not sufficient" for school employees.
"It doesn't teach how to respond emotionally and technically" to a potentially chaotic situation where young lives could be at stake, he said.
Dewhurst has a concealed handgun license and made his comments in a speech to the conservative Texas Public Policy Foundation.
Clay Robison, spokesman for the Texas State Teachers Association, said the state should spend more money on classroom instruction, not firearm instruction for teachers. The money Dewhurst is talking about would be better spent on equipping armed school security guards, he said.
"Teachers sign up to teach, not to be armed security guards in their classrooms," Robison said. "Even well-trained security guards with pistols are going to be at a disadvantage to a suicidal maniac with an assault rifle."
The prospects for his proposal weren't immediately clear. A spokesman for Sen. Joan Huffman, of Houston, leader of the Senate Republican Caucus, said she could not comment on Dewhurst's plan and its chances of passing the GOP-dominated chamber until the caucus meets next week.
Texas is a state where gun ownership is typically embraced. Concealed handgun license holders are allowed to bring weapons into the state Capitol and don't have to pass through security metal detectors.
Although state law generally bans guns from schools, school districts may grant teachers and staff permission to carry weapons on to campus if they are licensed.
But lawmakers don't pass every gun bill that gets proposed. In 2011, most of the state's lawmakers signed on in support of a bill allowing concealed weapons into college classrooms, but the bill failed without a final vote in the Republican-majority House.
Dewhurst said his plan would not be a mandate for more guns in schools, but would allow school districts to seek the state's help in guarding against a mass shooter.
Texas Gov. Rick Perry has said concealed handgun license holders should be allowed to carry their weapons wherever they want. Perry has a concealed handgun license.
Perry spokeswoman Catherine Frazier said Perry has called on schools to review emergency plans and "supports having a conversation during the legislative session about what we can do to strengthen school safety."
The Harrold Independent School District near the Oklahoma border is one of the few in Texas that allows school personnel with concealed handgun licenses to carry their weapons to school. The teachers and staff must first be approved by the school board and also take additional training on shooting accuracy, hostage situations and how to clear a classroom in a program designed for the school district.
Harrold schools Superintendent David Thweatt said he's heard from many Texas school districts about his program since the Newtown shootings. He said the program is cheaper than paying for an armed security guard.
"I'm getting a lot of calls from around the state," said Thweatt, who created his district's Guardian Plan in 2007.
"I think it's a good idea," Thweatt said of Dewhurst's idea. "One of the biggest objections to firearms in society is that some don't want people with that tool without some kind of extra training."