Lt. Gov. Dan Patrick of Texas publicly endorsed expanding the state’s background checks to private gun sales on Friday, defying the National Rifle Association — a group that had previously given the conservative an A-plus grade for his Second Amendment bona fides.

Mr. Patrick, a Republican who was elected to a second term in 2018, went so far as to say during an interview on Friday with The Dallas Morning News that he was “willing to take an arrow” from the gun lobby.

Mr. Patrick’s stance on expanding background checks followed a cycle of gun violence in the state, where gun culture is entrenched and transcends political affiliation.

It came less than a week after a gunman terrorized motorists near Odessa, Tex., killing seven people and wounding at least 21 more with an assault-style rifle that he obtained from a private seller in Lubbock, Tex., despite failing a background check in 2014 for a mental health issue. Earlier in August, 22 people were killed in a shooting rampage at a Walmart in El Paso in which a gunman targeted Hispanics.