The justices were aware of the historic nature of their undertaking, engaging in an extended 98-minute session of questions and answers that could yield the first definition of the meaning of the Second Amendment in its 216 years.
A key justice, Anthony Kennedy, left little doubt about his view when he said early in the proceedings that the Second Amendment gives "a general right to bear arms."
Several justices were skeptical that the Constitution, if it gives individuals' gun rights, could allow a complete ban on handguns when, as Chief Justice John Roberts pointed out, those weapons are most suited for protection at home.
"What is reasonable about a ban on possession" of handguns?" Roberts asked at one point.
But Justice Stephen Breyer suggested that the District's public safety concerns could be relevant in evaluating its 32-year-old ban on handguns, perhaps the strictest gun control law in the nation.
"Does that make it unreasonable for a city with a very high crime rate...to say no handguns here?" Breyer said.
Solicitor General Paul Clement, the Bush administration's top Supreme Court lawyer, supported the individual right, but urged the justices not to decide the other question. Instead, Clement said the court should allow for reasonable restrictions that allow banning certain types of weapons, including existing federal laws.
He did not take a position on the District law. Washington residents are not allowed to own handguns, period, CBS News correspondent Wyatt Andrews reports. And shotguns, which are allowed, are required to be kept unloaded and trigger-locked.
The court has not conclusively interpreted the Second Amendment since its ratification in 1791. The basic issue for the justices is whether the amendment protects an individual's right to own guns or whether that right is somehow tied to service in a state militia.
The amendment reads: "A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed."
While the arguments raged inside, advocates of gun rights and opponents of gun violence demonstrated outside court Tuesday.
Dozens of protesters mingled with tourists and waved signs saying "Ban the Washington elitists, not our guns" or "The NRA helps criminals and terrorist buy guns."
Members of the Brady Campaign to Prevent Gun Violence chanted "guns kill" as followers of the Second Amendment Sisters and Maryland Shall Issue.Org shouted "more guns, less crime."
A line to get into the court for the historic arguments began forming two days earlier and extended more than a block by early Tuesday.
The high court's first extensive examination of the Second Amendment since 1939 grew out of challenge to the District's ban.
Anise Jenkins, president of a coalition called Stand Up for Democracy in D.C., defended the district's prohibition on handguns.
"We feel our local council knows what we need for a good standard of life and to keep us safe," Jenkins said.
But, Andrews reports that Washington Mayor Adrian Fenty said: "This is a public saftey case. Handguns represent a disproportionate number of crimes in the District of Columbia."
Genie Jennings, a resident of South Perwick, Maine, and national spokeswoman for Second Amendment Sisters, said the law banning handguns in Washington "is denying individuals the right to defend themselves."
Even if the court determines there is an individual right, the justices still will have to decide whether the District's ban can stand and how to evaluate other gun control laws. This issue has caused division within the Bush administration, with Vice President Dick Cheney taking a harder line than the administration's official position at the court.
The local Washington government argues that its law should be allowed to remain in force whether or not the amendment applies to individuals, although it reads the amendment as intended to allow states to have armed forces.
The City Council that adopted the ban said it was justified because "handguns have no legitimate use in the purely urban environment of the District of Columbia."
Dick Anthony Heller, 65, an armed security guard, sued the District after it rejected his application to keep a handgun at his home for protection. His lawyers say the amendment plainly protects an individual's right.
The last Supreme Court ruling on the topic came in 1939 in U.S. v. Miller, which involved a sawed-off shotgun. Constitutional scholars disagree over what that case means but agree it did not squarely answer the question of individual versus collective rights.
Given the Court's strong conservative makeup, it is likely that both a right to own, possess and use a firearm and the government's right to restrict that ownership, possession will survive the Heller case, says CBS News legal analyst Andrew Cohen. The only thing that remains reasonably unpredictable and mysterious is thein conjuring up the legal standard that will govern review of gun control legislation.
Chief Justice John Roberts said at his confirmation hearing that the correct reading of the Second Amendment was "still very much an open issue."