“Essentially, we are telling states who are responsible in the requirements that they place on their concealed-carry permits that that doesn’t matter anymore,” said Representative Eric Swalwell, Democrat of California.

The measure, which has been co-sponsored by 210 Republicans and three Democrats, was expected to win passage in the Republican-controlled House as soon as next week. But its fate in the Senate is far less certain. Republicans control only a narrow majority in that chamber, where any legislation would need to pick up Democratic votes.

As passed by the committee, the law would treat a concealed-carry permit like a driver’s license, allowing individuals permitted by any one state to carry a concealed gun into any other, regardless of the discrepancies between the states’ permitting criteria. Each state would still be allowed to determine those criteria for its own citizens and all permit holders would be required to abide by local laws.

The measure also allows visitors to national parks, wildlife refuges and other federally administered lands to legally carry concealed firearms. And Republicans passed an amendment to the bill that would allow off-duty police officers and qualified retired officers to carry guns in school zones.

Wednesday’s debate revisited arguments that have grown familiar in recent years as Congress has deadlocked over how, if at all, to address a series of increasingly deadly mass shootings. The committee, one of the House’s most ideologically divided and largely split between Republicans from suburbs and rural areas and mostly urban Democrats, showed that little has changed in the wake of the Las Vegas and Sutherland Springs shootings, which took dozens of lives and left hundreds injured.