AUSTIN, Tex. — Four days after the latest school shooting left 10 people dead at a Texas high school, Gov. Greg Abbott — torn between his state’s reluctance to pass new gun control laws and his own frustration at the grim and growing tally of young deaths — convened on Tuesday the first in a series of round-table discussions on ways to help protect schools from gun violence.

“Whether you are a Republican or Democrat, whether you are pro-gun or believe in more gun regulations, the reality is we all want guns out of the hands of those who would try to murder our children,” the Republican governor said as he opened the first day of talks in the State Capitol with lawmakers, school administrators and law enforcement officials. “The question is what are we, the leaders of Texas, going to do to prevent this from happening again?”

During the afternoon-long session, school experts and law enforcement officials found broad agreement on a host of preliminary ideas, some of which could be put into place without legislative approval before the start of school, in August.

The group’s recommendations included increasing parental accountability and encouraging students to pass along information about potentially violent students. The governor strongly endorsed proposals to expand and strengthen training for school officials, create threat assessment and mental intervention programs, and evaluate entrances and exits to make schools more secure. Discussion of guns and gun laws was reserved for the session on Wednesday.