Two conservative justices said they would have heard the case and struck down the ban.
The court, though, left in place a lower court ruling that found that local governments have leeway in deciding how to regulate firearms. The federal appeals court in Chicago upheld the city of Highland Park's 2013 gun law that bans semi-automatic weapons and large-capacity magazines.
In October, the federal appeals court in New York largely upheld similar laws in Connecticut and New York, among a handful of states that ban semi-automatic weapons.
The Supreme Court has repeatedly turned away challenges to gun restrictions since two landmark decisions that spelled out the right to a handgun to defend one's own home.
CBS News correspondent Jan Crawford reports that in 2008 the Supreme Court struck down a handgun ban in the District of Columbia, ruling that the Second Amendment protects a person's right to bear arms for self-defense in the home.
But in the years since, lower federal courts have narrowly applied the landmark decision-allowing what they consider reasonable gun restrictions -- bans on large capacity semiautomatic firearms, like the commonly owned AR-15.
Justice Clarence Thomas, joined by Justice Antonin Scalia, said the Chicago appeals court ruling "flouts two of our Second Amendment precedents." Without mentioning any mass shootings in California and elsewhere that involved semi-automatic guns, Thomas said the weapons ban "is highly suspect because it broadly prohibits common semi-automatic firearms used for lawful purposes" by roughly five million Americans.
"The overwhelming majority of citizens who own and use such rifles do so for lawful purposes, including self-defense and target shooting," Thomas wrote.
The case had been under consideration at the high court for two months, but the delay in dealing with it now appears mainly due to waiting for Thomas to finish his opinion.
The appeal filed by Dr. Arie Friedman and the Illinois State Rifle Association argues that Highland Park has violated their constitutional rights by banning some of the most popular semi-automatic guns in the United States, as well as ammunition magazines of more than 10 rounds.
Even though lower courts have mainly upheld gun restrictions, the Highland Park case arises out of a decision by the federal appeals court in Chicago that struck down the only statewide ban on carrying concealed weapons, in Illinois.
In 2013, when state lawmakers reacted to the court ruling by making it legal to carry a gun, they gave cities around the state 10 days to come up with local restrictions on assault weapons, or forfeit their right to do so.
Highland Park was one of fewer than 20 municipalities, all in the Chicago area, to enact regulations or bans, according to the rifle association.
The city's assault weapons ban was upheld by the appeals court in a 2-1 decision.
Judge Frank Easterbrook wrote for the court that there is a "substantial benefit" to the Highland Park ordinance if it makes the public feel less at risk from a mass shooting. Variations of the Bushmaster AR-15, one of the guns specifically banned by Highland Park, were used in the Newtown, Connecticut school massacre and the theater shootings in Aurora, Colorado.
The gun control laws that the appeals court in New York upheld in October were passed after the 2012 massacre in Newtown.
Seven states and the District of Columbia have enacted laws banning assault weapons. The others are California, Hawaii, Maryland, Massachusetts and New Jersey, according to the Law Center to Prevent Gun Violence. In addition, Minnesota and Virginia regulate assault weapons, the center said.
The case is Friedman v. Highland, 15-133.
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