WASHINGTON—The Supreme Court seemed likely to rule for the first time that gun possession is fundamental to American freedom, a move that would give federal judges power to strike down state and local weapons laws for infringing on Second Amendment rights.

At oral arguments Tuesday, the court considered whether its 2008 decision voiding the District of Columbia handgun ban should be extended to the rest of the country. Because Washington is federal territory and not part of a state, the legal basis for imposing federal constitutional...