The bill would allow permit holders to bring their guns into restaurants that serve liquor.
It cleared the House Business and Industry Committee on a bipartisan 6-4 vote Thursday night.
The sponsor, Republican Rep. Zach Cook of Ruidoso, eliminated the section of the bill that would have allowed permit holders to bring their guns into bars.
"There was a lot of opposition to that," he said afterward.
Rather than risking defeat in his first committee hearing on the bill, Cook decided not to press for carry rights in bars.
Convenience to permit holders was the main reason he cited for trying to enable them to bring guns into restaurants.
Cook said his constituents told him they do not want to remove their concealed guns when going to dinner at an establishment that serves alcohol.
Those carrying guns are not supposed to drink, however. They are restricted by their permits from consuming alcohol when armed.
Two Democrats on the committee joined four Republicans in voting for Cook's bill. The Democrats who supported it were Reps. Dona Irwin of Deming and Debbie Rodella of Espanola.
Cook's proposal, House Bill 137, was waiting for consideration in both the House Industry and Business Committee and the House Judiciary Committee on Friday, according to the Legislature's bill tracker.
He has been trying since 2011 to expand the rights of people with concealed-carry permits.
Cook's first try was sweeping but unsuccessful. He authored a bill to allow people with carry permits to bring their guns into public schools, liquor establishments, college campuses, buses, and state parks and recreation areas.
Gov. Susana Martinez, also a Republican, said she did not favor guns in schools.
Cook then streamlined that bill too, but it died in a committee.