Secretary of Homeland Security Alejandro Mayorkas said the department is "horrified by this callous act of violence," in a statement Wednesday.

Mayorkas said one Border Patrol agent was injured in the crossfire.

"We are grateful for the courageous members of our Border Patrol, many of whom are part of the Uvalde and surrounding communities, who immediately responded to the scene along with local and state law enforcement," Mayorkas said.

He added, "Without hesitation, they put themselves between the shooter and students to end the bloodshed and administer medical aid. Without question, their heroism yesterday saved lives."

The department will continue to coordinate with local, state and federal partners, Mayorkas said.

"As we pray for the families and loved ones and recognize the bravery of frontline law enforcement personnel, we must redouble our collective efforts to make our communities safer," Mayorkas said.

Texas state Sen. Roland Gutierrez called on lawmakers to act on gun control, specifically calling on them to look into an assault weapons ban at the federal level, in an interview on ABC News Live Wednesday.

"We have to make sure that we're creating laws in the state of Texas, as well as at the federal level, so that we can stop access to these types of militarized weapons," Gutierrez said on ABC News Live.

"I know my district -- there's nobody in this district that goes hunting with an AR-15," Gutierrez said, referring to the assault weapon the alleged shooter had purchased two days before the shooting.

Gutierrez called on the U.S. Senate to break the filibuster and pass legislation in order to stop seeing "these types of militarized weapons."

"We have young, confused men, young men violating lives across this country and violating families across this country."

He added, "It is high time that we do something. My heart goes out to the people in my community here in the valley, but we've got to take that to another level and do something now. Because if we can't do something, then what are we? What are we sending people off to Washington for? What are we sending people up to Austin for? We've got to do more."

Senate Majority Leader Chuck Schumer gave a passionate speech on the Senate floor Wednesday, calling gun violence “a plague upon this nation."

"The problem in the Senate is simple too many members on the other side of the aisle are disconnected from the suffering of the American people, too many members on that side care more about the NRA than they do about families who grieve victims of gun violence," Schumer said.

Schumer criticized Republicans for their opposition to gun control legislation.

"Republicans don't pretend that they support sensible gun safety legislation. They don't pretend to be moved by the fact that 90% of Americans, regardless of party, support something as common sense as background checks," Schumer said.

Schumer said he aches for the families of those killed in Texas and urged Republicans to act "for the sake of these children."

"To my Republican colleagues: Imagine if it happened to you. Imagine if this was your kid or your grandkid. How would you feel? Could you ever forgive yourself for not supporting a simple law that would make these mass shootings less likely? Please, please, please dammit. Put yourself in the shoes of these parents for once," Schumer said.

-ABC News' Trish Turner

Texas Gov. Greg Abbott will hold a press conference Wednesday at 1:30 p.m. ET to discuss the state's response to the Robb Elementary School shooting.

The governor will be joined by state officials including Lt. Gov. Dan Patrick, Texas state House Speaker Dade Phelan, U.S. Sens. John Cornyn and Ted Cruz and U.S. Rep. Tony Gonzalez.