May 30 (Reuters) - The Republican-controlled Texas Senate voted on Saturday to allow the licensed carrying of concealed handguns in most state university buildings. The measure includes a caveat that lets college presidents designate "gun-free zones" on their campuses. Passage by the Republican-dominated House of Representatives is expected on Sunday and would send it on to Republican Governor Greg Abbott to be signed into law. The bill was a priority for gun rights activists, even though many universities statewide opposed it. Senator Rodney Ellis, a Democrat from Houston who voted against the bill, said in a statement that the passage reflected "misplaced priorities." Both chambers had passed their own versions of the bill.