By Jon Herskovitz

AUSTIN, Texas, May 22 (Reuters) - Days after 10 people were shot to death at Texas high school, Governor Greg Abbott met with politicians and school administrators on Tuesday to consider proposals to stem school violence in a state where gun-control measures usually sink in the Republican-controlled legislature.

About 20 people, including those who support arming teachers, attended the first of three days of meetings in the state capital, Austin, following the fourth-deadliest U.S. school shooting this year at Santa Fe High School in Santa Fe, Texas, on Friday.

"The problem is that innocent people are being shot and that must be stopped," Abbott, a staunch gun rights supporter, told reporters before the meeting that lasted more than two hours and was held behind closed doors.

Among the measures coming out of the meeting that Abbott said he would like to see implemented quickly were expanding school safety training programs, bolstering threat assessment systems and expanding a pilot program designed to screen for students who might be a threat to themselves or others.

"We did more today than talk. We came up with some very solid solutions," Abbott told reporters. Another measure under consideration was setting up a system to monitor social media for warning signs of an attack.

The Republican-controlled legislature is out of session until January 2019, making it nearly impossible for the state to implement and fund any major changes that come out of this week's talks.

The Texas Democratic Party in a statement called the roundtable meetings "theatrics" and chastised Abbott for holding the discussions behind closed doors.

Abbott, a Republican, has vowed that any changes to state laws would "protect Second Amendment rights."

The Second Amendment of the U.S. Constitution enshrines the

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