ATLANTA — With their first opportunity to address gun laws since a lone shooter killed 20 Connecticut schoolchildren in December, Georgia lawmakers decided to do nothing. At least until next week.

A Bartow County Republican wants local school boards to be able to designate school administrators who can carry weapons, provided they are trained to use them. Rep. Paul Battles told his colleagues Tuesday that his idea would give local authorities a way to protect students without forcing them to spend money on armed officers.

“I wish House Bill 35 were not necessary,” he said, “but I’m afraid it is.”

But Alan Powell, the Hartwell Republican who leads the House panel that writes public safety law, told the sponsor after more than two hours of debate that he will delay a vote until a special subcommittee can work through details of the proposal. Powell said he wants consensus on the training that would be required, the kind of weapons that would be allowed and effects on schools’ liability insurance.

The delay and the lengthy hearing that preceded it underscore the complicated policy questions and sensitive political calculations at play since the mass shooting at Sandy Hook Elementary School. The debate also comes just days after a non-fatal shooting at Price Middle School in Atlanta.

Gov. Nathan Deal and the Republican-dominated legislature have made clear that they will not entertain new restrictions on the manufacture, sale and possession of firearms and ammunition. But GOP leaders are less clear about how they want to handle a range of proposals that could expand gun presence in public places.

Several tea party conservatives have introduced bills that would roll back all existing restrictions on where Georgia residents can carry concealed weapons, including in schools and churches. None of those proposals have had a committee hearing, as top Republicans like House Speaker David Ralston have carefully singled out Battles’ bill as “a reasonable approach.”

Battles framed his proposal Tuesday as a “school safety bill, not a gun bill.”

He and several members noted that many Georgia high schools already have armed officers, either paid directly by school systems or, in some cases, local law enforcement agencies. But he said “there is no money” — or at least the political will to find the money — to make that a statewide practice. The next best strategy, Battles argued, is to expand administrators’ responsibilities, as long as the decisions are made locally.