Locally in port, the Captain of the Port (COTP) sets MARSEC but he MAY delegate to a local Port Director in the case of a local incident. For example, if there was a shooter in Fourchon, it would start with the Fourchon Port Police and the COTP would sign off on it later.
Nationally, the Director of the Ministry of Homeland Security sets it through the Commandant of the Coast Guard.
BTW, the Coast Guard is responsible for the Air defense of Washington D.C. Let us hope it is more efficient than NMC. HAHAHAHA!