WASHINGTON — Amid a growing clamor for action to address a rash of mass shootings, Sen. Ted Cruz pushed back hard Tuesday against demands for restrictions on assault weapons, calling instead for a fresh look at a bill aimed at keeping guns away from criminals.

"If the objective is to stop violent crime, we should focus on stopping the violent criminals and rapists and murderers," he said in a call with reporters as Texans go to the polls on primary day. "Texans want to stop the criminals. Texans do not want Washington politicians disarming law-abiding citizens."

Cruz and Sen. Chuck Grassley, R-Iowa, pushed a bill in early 2013 after a school shooting in Newtown, Conn., as an alternative to Democratic efforts to ban so-called assault weapons and high-capacity ammunition magazines. The bill also includes $300 million to beef up school security — funds that Cruz contends were cut by the Obama administration, leaving the students at a Parkland, Fla., high school vulnerable to a rampage last month that left 17 dead.

"What is not effective is the repeated efforts of Democrats to undermine the Second Amendment rights of law-abiding citizens," said Cruz, who is expected to coast to nomination to a second term in Tuesday's GOP primary. Rep. Beto O'Rourke, D-El Paso, is expected to win the Democratic nomination.

Gun control and approaches to school safety are a major dividing line between them.

Cruz sidestepped questions about whether he would support a ban on high-capacity ammunition magazines that allow shooters such as the Newtown killer to continue firing without having to pause to reload. And he declined to say whether he supports a ban on bump stocks, the device used in the Las Vegas concert massacre last fall that let the shooter fire at near automatic rates.

He noted only that automatic weapons have been banned for 70 years, that the ATF allowed the sale of the device during the Obama administration and that President Donald Trump has ordered a ban.

Republican Texas Sen. John Cornyn also called on Democrats on Tuesday to drop their “gun control demands,” pitching his own bill to improve the federal background check system for gun purchases.

Cornyn introduced the “Fix NICS Act” with Connecticut Sen. Chris Murphy following the Sutherland Springs church shooting in November. The measure, named after the National Instant Background Check System, would penalize federal agencies that fail to report records and incentivize states to send criminal history records to the FBI database used for gun purchases.

Cruz has not signed on to the Cornyn-Murphy bill, which has 49 co-sponsors.

“We should start with what's achievable and what will actually save lives, and that describes the Fix NICS bill,” Cornyn said from the Senate floor Tuesday. “This bill could easily pass the Senate. It's already passed the House. And the president would sign it, as he told me when he called me last Thursday night.”

Devin Kelley, who killed 26 people in the First Baptist Church of Sutherland Springs, including a pregnant woman and her fetus, would not have been allowed to purchase a gun from a store if the Air Force had reported his court-martial and conviction for domestic violence to the database.

Cruz and Cornyn have repeatedly said that their bills would have prevented Kelley from buying a gun.

Cruz touted the $300 million his bill would provide for school safety, suggesting that some of the funds might have meant another officer or metal detectors at the Florida high school. One armed deputy was on site and failed to confront the killer.

Not far enough

Trump backs Cornyn’s background check bill, but some lawmakers say it doesn’t go far enough to curb gun violence. Democrats and a handful of Republicans have suggested raising the age to 21 for all gun sales, requiring background checks on sales at gun shows and online, and allowing law enforcement to temporarily block a potentially dangerous individual from purchasing a gun.

But Cornyn argues that his bill has the most broad, bipartisan support of any gun measure.

“People want to make this bill a Christmas tree, trying to decorate it with other legislative ornaments that look nice to their political base but stand no chance” in the Senate or House, Cornyn said. “It's political posturing.”

Congress could consider a more expansive universal background check bill by Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa. Toomey told The Associated Press that Trump supports making that bill the “core legislative vehicle.”

The Manchin-Toomey bill, introduced in 2013 after the Sandy Hook elementary school massacre in Newtown, would have expanded background checks for gun show sales and online sales between private individuals.

A Quinnipiac University poll released last month found that 97 percent of voters support background checks on all gun buyers — something Cornyn's bill doesn't address.

"It swept far beyond commercial sales, and that was one of the concerns," Cornyn said last week of the Manchin-Toomey bill.

Cornyn’s measure passed through the House in December. But it was attached to a bill that would allow use of a concealed carry permit from any state to be used anywhere. That’s a top NRA priority and one that Cornyn supports, but he and others have noted that opposition is widespread and it is unlikely to pass in the Senate.

Public opinion

A Quinnipiac University Poll released Tuesday found that American voters oppose allowing teachers and school officials to carry guns on school grounds by a wide margin: 58 percent to 40 percent.

But voters overwhelmingly (82-14 percent) support having armed security officers in schools.

Support is nearly the same for restricting sales of guns to people 21 and older.

Sens. Dianne Feinstein, D-Calif., and Jeff Flake, R-Ariz., introduced a bill to raise the minimum age to purchase all guns for 18 to 21. Federal law requires buyers to be 21 to purchase a handgun and 18 to purchase a long gun from a licensed dealer.

And support remains roughly 2-to-1 in favor of stricter gun laws, including 61-35 percent support for a nationwide ban on the sale of assault weapons. That’s about the same as the support for a ban on high-capacity ammunition magazines that allow shooters to continue firing without pausing to reload.

The public is evenly split on whether to ban semi-automatic rifles.

Support is strongest for banning possession of a gun by anyone with a restraining order against them for stalking or domestic, sexual or repeat violence.

“The outcry on guns continues, and voters say it’s on you, Republicans, to make the change,” said Tim Malloy, assistant director of the poll.