The Texas Senate approved a bill on Thursday that would allow people to carry concealed handguns on college campuses.

Supporters say the measure, which has the backing of gun rights groups, will help licensed students over 21 better protect themselves. The Senate voted on the measure along party lines, and the Republican-controlled House is taking it up next week.

But the move to legalize licensed weapons on campuses has prompted opposition from law enforcement and university leaders, including University of Texas System Chancellor William McRaven, a retired Navy admiral who oversaw the operation that killed Osama bin Laden.

“I continue to remain apprehensive about the effects of this legislation on UT System institutions and our students, staff, patients and visitors,” McRaven said in a statement to TIME. “I continue to hear from students, parents, staff and faculty about their uneasiness related to this legislation. In light of this, it is my responsibility to continue to express our concerns as the Senate bill goes to the House and the House bill goes through the process.”

While most states either ban concealed arms on campus or leave the decision to colleges and universities individually, seven states have provisions that allow for concealed weapons on public post-secondary campuses, according to the National Conference of State Legislatures. Several Republican-held legislatures, including in Florida and Montana, are also considering easing their restrictions on weapons on campuses.

While the Texas legislature has failed to pass similar bills three times since 2009, this bill has strong backing in the House and Governor Greg Abbott has expressed his support.

Still, student groups and higher education leaders are voicing their opposition.

“There is great concern that the presence of handguns, even if limited to licensed individuals age 21 or older, will lead to an increase in both accidental shootings and self-inflicted wounds,” McRaven wrote in an open letter to state leaders in January.

— Charlotte Alter contributed reporting.

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Write to Noah Rayman at noah.rayman@time.com.