Just to clear up some confusion, the Moritas seen in Invasion and Traitor of Mars should be considered the Mk. IV series. For some bizarre reason the mobile game Starship Troopers: Invasion - Mobile Infantry had the Morita from Invasion listed as Mk. I, and the SAW variant listed as Mk. III. Given that we've already had Moritas Mk. I, II, & III from the first three films; I think it's safe to say that the mobile game got it wrong and should not be considered accurate. Therefore I think we can agree that the Moritas from Invasion and Traitor of Mars are indeed the Mk. IV series even if there hasn't been any official confirmation, and I've updated the articles to reflect that. Unfortunately the most recent games Terran Command and Extermination also got the naming wrong (presumably from the incorrect information from the mobile game and possibly even this wiki). So hopefully after fixing the articles here the recent games will also fix the names to be more accurate to the lore.
(UPDATE):
After conducting further research I've discovered even more discrepancies. In Traitor of Mars the troopers' HUD shows their weapon listed as "MK I AR", which would give possible credence to the Invasion mobile game's naming scheme for the weapons. However the troopers' HUD also shows their weapon as MK I AR when they have the SAW equipped, not the Mk. III as stated in the Invasion mobile game. Additionally the original Morita from the first film is listed as the Mk2 in the 2005 video game but as the MK1 in Extermination. Not to mention of course the Marauder Mk4 rifle from the 2005 game. This naming scheme is all over the place with no consistency and a bunch of glaring contradictions. I think it's safe to say at this point that we can't take any of the games as official canon when it comes to the names of the weapons, as they make no logical sense whatsoever. I believe the best course of action in order to keep everything consistent is to get rid of the Mk. designation all together and just go by Morita I, II, III, & IV series; with the Morita IV series being the guns in Invasion and Traitor of Mars including the SAW as I stated previously. We can of course mention their Mk. designation in their individual pages. Out of universe the obvious explanation is that the names got messed up, in-universe however the best thing that I can think of is that that Mk. designation is for minor iterations of the same gun, and not a separate series.