A day after the Senate voted to begin debate on new gun control measures, the Supreme Court is expected to consider a new appeal aimed at loosening state restrictions on firearms.

The justices will meet in private today to discuss adding new cases for the term that begins in the fall. Among them is an appeal of a federal court ruling that upheld New York’s strict licensing scheme for carrying concealed weapons in public.

The National Rifle Association and 20 states are backing an appeal by five New York residents who claim that the state law violates their constitutional gun rights. The challenge comes nearly five years after a landmark Supreme Court decision in favor of gun rights, and four months after a gunman killed 20 children and six adults in Newtown, Conn.

The court could say as early as Monday whether it will hear the case.

Legal scholars say the issue of whether people have a right to be armed in public is likely to win high court review at some point. The court’s 2008 decision in District of Columbia v. Heller focused mainly on the right to defend one’s own home, but it left for another day how broadly the Second Amendment may protect gun rights in other settings.

In November, less than three weeks before the Newtown shootings, the 2nd U.S. Circuit Court of Appeals in New York upheld a state law that requires those who want to carry handguns to show a special need for self-protection. Other states with gun laws like New York’s include California, Hawaii, Maryland, Massachusetts and New Jersey.

Another federal appeals court in Richmond, Va., has since upheld the Maryland law, while challenges are pending to the laws in California, Hawaii and New Jersey.

Alan Gura, an Alexandria, Va.-based lawyer who is representing the New Yorkers, as well as the challengers in several other states, said that by upholding such state laws, lower courts are undermining constitutional protections for gun owners.

Gura said the appeals-court rulings on the New York and Maryland laws, “if left unchecked, will accelerate the lower courts’ resistance” to the Supreme Court’s endorsement of gun rights.