It was no surprise that the proposals presented on Wednesday by Mr. Abbott, who is running for re-election this year, were heavily skewed toward hardening schools and bolstering campus security and mental health programs, while failing to endorse any significant new restrictions on gun ownership or sales.

Mr. Abbott is a staunch gun rights advocate who has urged Texans to buy more guns. And he is governor in a state where polling indicates that far more Republicans — the party that controls every major political office in Texas — blame mass shootings on failures of the mental health system than they do on the failure to pass more gun laws.

A series of round tables on school safety organized by Mr. Abbott after the Santa Fe shooting excluded most influential gun control and teachers’ organizations, and were seen by many as stacked against any significant tightening of gun laws.

Ed Scruggs, vice chairman of Texas Gun Sense, a nonprofit gun violence prevention group, said that Mr. Abbott’s proposals were “not enough to really tackle the issue of gun violence and keep guns out of the hands of people who shouldn’t have them.”

Mr. Scruggs, the only gun control advocate to take part in the school safety round tables, called the governor’s failure to support background checks for all gun purchases “a missed opportunity.” But he said he was encouraged that Mr. Abbott was open to a red flag law, and that he had endorsed tougher gun storage laws.

Polls conducted by the University of Texas and The Texas Tribune have shown wide support among both Republicans and Democrats in the state for background checks on all gun sales, a measure that would eliminate the ability to purchase firearms in person or online from private sellers without the standard F.B.I. check on the buyer’s criminal, domestic abuse and mental health background.

But seven times as many Texas Republicans blame mass shootings across the United States on mental health system failures as on gun laws, a University of Texas/Texas Tribune poll found in October 2017. The same poll indicated that five times as many Republicans in the state believed that more guns would make the country safer than those who believed that they would make it less safe.