18 U.S. Code §930 - Possession of firearms and dangerous weapons in Federal facilities specifically prohibits possession of a firearm or other dangerous weapon in a Federal facility, the latter being defined as "a building or part thereof owned or leased by the Federal Government, where Federal employees are regularly present for the purpose of performing their official duties."
The term “dangerous weapon” means "a weapon, device, instrument, material, or substance, animate or inanimate, that is used for, or is readily capable of, causing death or serious bodily injury, except that such term does not include a pocket knife with a blade of less than 2½ inches in length."
Notice of the provisions of subsections (a) and (b) shall be "posted conspicuously at each public entrance to each Federal facility, and notice of subsection (e) shall be posted conspicuously at each public entrance to each Federal court facility, and no person shall be convicted of an offense under subsection (a) or (e) with respect to a Federal facility if such notice is not so posted at such facility, unless such person had actual notice of subsection (a) or (e), as the case may be."
Just to note, Subsection (a) states this "shall not apply to the possession of a firearm or other dangerous weapon by a Federal official or a member of the Armed Forces if such possession is authorized by law." How that would be determined--i.e. if a state-issued license is sufficient--is unknown. https://www.law.cornell.edu/uscode/text/18/930