Abbott has occasionally talked about tightening Texas gun laws.

In the seven years that Greg Abbott has served as governor of Texas, dozens of people have been killed in mass shootings across the state. In a few cases, his administration has responded to the violence by indicating an openness to tightening the state’s gun laws.

But not much has changed, and those laws remain some of the least restrictive in the United States.

In May 2018, in response to shootings in Sutherland Springs and Santa Fe that left a total of 36 people dead, Mr. Abbott issued a 43-page report calling for more school security and preparation for “active shooters on campus,” among other measures.

The Republican governor’s report also asked state lawmakers to “study the possibility of creating” a so-called red flag law, one that would allow the police to temporarily confiscate firearms from people a judge considers to be a danger to themselves or to others.

The results of Mr. Abbott’s report included a $1 million item in the state’s budget for the Department of Public Safety to promote safe gun storage, as well as a state law abolishing a cap on the number of school marshals who are allowed to carry guns on public school campuses.

But, unlike Florida, where state lawmakers passed a red flag law weeks after 17 people were fatally shot at Marjory Stoneman Douglas High School in 2018, the idea for a similar measure in Texas died in a state legislature committee. One reason was public opposition from Mr. Abbott’s own lieutenant governor, Dan Patrick.

“Regarding the topic of ‘Red Flag’ laws, which was discussed today in the select committee, I have never supported these policies, nor has the majority of the Texas Senate,” Mr. Patrick said in a statement in July 2018.

A similar pattern played out in the summer of 2019, after a gunman killed 22 people at a Walmart in El Paso and another killed seven others and wounded at least 21 more in Odessa.

A few days after the Odessa massacre, Mr. Patrick publicly endorsed expanding the state’s background checks to private gun sales, telling The Dallas Morning News that he was “willing to take an arrow” from the gun lobby to champion such a measure.

But Mr. Patrick later went quiet on the idea of background checks. And last year, Mr. Abbott, whose policies have been drifting rightward in recent years, signed a wide-ranging law ending a requirement for Texans to obtain a license to carry handguns. Now, virtually anyone over the age of 21 is allowed to do so.

In a news conference on Wednesday, Mr. Abbott said that although the gunman who killed 19 children in Uvalde had no known history of mental issues, he believed that the area near the school lacked sufficient access to mental health care. “We as a state, we as a society, need to do a better job with mental health,” he said.

He did not make any specific proposals for legislation that would address gun violence.