I dont think any of the norkom merchant marine vessels are civillian operated and while it was’nt a war ship a north korean vessel was stopped and boarded for supplying no dong missile bodys to Iran , I believe.
As for the interception , I would think only in the case just prior to going to war , you would be advised to do that.
How about if a blockade has been declared? Was the US legally justified in intercepting Russian shipping bound for Cuba at the time of the missile crisis? (Can’t recall if any ships were actually intercepted, I think the Russians turned back of their own accord.)
Gfactor is correct in citing the UN Convention on the Law of the Seas (which to further complicate the matter, has not been ratified by the U.S.), but the article he’s citing explicitly covers only ships “other than a ship entitled to complete immunity in accordance with articles 95 and 96.” The OP is explicitly asking about military ships, which are accorded immunity under article 95 of said convention, as he pointed out. That excludes them from the scope of application of the quoted provision.
Because of this immunity, I think intercepting a foreign military vessel would almost always (i.e., if not justified by the special circumstances of emergency) be an act of war. Maybe it could be justified under the right of hot pursuit (article 111 of the convention), which applies if a ship has been found in a country’s internal or teritorial waters of a state violating the laws of that state. Hot pursuit makes it possible to go after the ship even if it reaches the high seas during the hunt.