First, even without the Second Amendment, the federal government still would not have the authority to regulate gun ownership within the borders of a state. The Constitution does not delegate this power to the federal government; therefore it remains with the states and the people.
Secondly, the language of the amendment itself defines much greater restriction on federal power. “The right of the people to keep and bear Arms, shall not be infringed.”
Infringe – v: Act so as to limit or undermine (something); encroach on.
The federal government may not constitutionally act in a way that even limits the right to keep and bear arms.