Well, the 2nd Amendment clearly says that “Congress shall make no law...”. It doesn’t say anything about the President, so technically he is correct. It won’t violate the 2nd Amendment, it will violate Article I, Section 1 of the Constitution, which vests lawmaking powers ONLY in the hands of Congress.
That must be in the US Constitution 2.0. I've never read any such language in the 2nd Amendment in the present US Constitution. It's in the 1st. But the 2nd says "SHALL NOT BE INFRINGED." Government infringes that right every day, so they might as well change the Constitution.
Only Congress can make laws. Presidents do not.
"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."
The Congress is not mentioned in the Second Amendment. The right of the people to keep and bear arms is constitutionally protected (hah!) from infringement by any branch of government.