The bill, declared all but dead in the House last week, received preliminary Senate approval on a 20-10 vote after 90 minutes of debate, the Houston Chronicle reported Wednesday.
If the Senate gives the measure final approval it will go back to the House where it died last week because of failure to meet a debate deadline.
The measure's sponsor, Sen. Jeff Wentworth, R-San Antonio, said he introduced the bill because he didn't want to see a repeat of the 2007 Virginia Tech massacre at a Texas institution.
"I would feel personally guilty if I woke up one morning and read that something similar had occurred on a Texas campus," Wentworth said.
Only 11 U.S. universities currently permit handguns on campus, the Chronicle says.
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