The actor addressed a swarm of paps Saturday who were hounding him in Manchester, VT, where he and his family have been laying low since the fatal incident ... but have been getting followed around, including on the open road, where the Baldwin family literally pulled over to confront the photogs ... whom Alec says made his kids cry.

Alec came at them head-on with none other than his wife, Hilaria, at his side ... and they spoke their piece on where things stand, without divulging too much about the investigation.

Check out the video ... from the looks of it, the convo was pretty tense, albeit courteous. AB demands to know what the paparazzi wanted to know -- so that they could get off his back, and they sounded off one by one. On where things stand as the probe into this matter unfolds ... Alec said he couldn't discuss details, on orders of the Santa Fe Sheriff's Office.

He did say Halyna was his friend, and that he took her out to dinner upon arriving to shoot "Rust." Alec also characterized the crew as "well-oiled," noting the accident is obviously shocking and devastating to him. He also touched on how Halyna's family is doing ... saying they're mortified, but that he's in touch with them quite often. Ditto for the authorities.

One major takeaway from his interview is the fact Alec spoke on what should happen with firearms on movie sets going forward ... he fully supports tightening up safety measures, and possibly banning real guns/live ammo altogether, while acknowledging he isn't a pro on that.

It's interesting ... Alec asked an open-ended question that seems to show where his head's at as far as consequences -- wondering how many real guns and bullets have been fired on film/TV sets over the past several decades, mostly without incident. In his mind ... a lot.

Up until now, Baldwin has only spoken about the tragedy once in his own words -- but it was via Twitter, and not in the flesh.

Shortly after the shooting took place, he issued a since-deleted statement saying, "There are no words to convey my shock and sadness regarding the tragic accident that took the life of Halyna Hutchins, a wife, mother and deeply admired colleague of ours. I'm fully cooperating with the police investigation to address how this tragedy occurred."

He added, "I am in touch with her husband, offering my support to him and his family. My heart is broken for her husband, their son, and all who knew and loved Halyna."

Baldwin has also been retweeting articles that dissolve him of responsibility -- noting he was simply handed a gun that he was told was "cold" ... and that he was only doing his job as an actor, relying on others to have properly checked it to make sure it was safe.

Those retweets, however, have also since been erased from his timeline -- it seems the guy figures saying less is best at this moment ... especially since a criminal investigation is still ongoing in New Mexico, and nobody has been ruled out for potentially being charged.

Alec touched base with Halyna's widowed husband, Matt, and their young son not too long after her death ... meeting them at a hotel in Santa Fe and embracing them. He looked as somber then as he did just recently while spotted out with his own family in New England.

You can see he's absolutely torn up about it ... just as he was on the actual day it happened, when he was photographed making calls on a nearby road and bawling his eyes out.

As you know by now ... how this all came to be is well-documented. Alec was rehearsing for a scene in a church on set, in which he was apparently going to be drawing his weapon for a gunslinging standoff of some sort.

While whipping the gun out, he pulled the trigger ... causing it to go off and fire a real bullet, which (for some reason) had been lodged inside prior to them starting work again. The bullet hit Halyna and director Joel Souza, who were standing close to Alec, near the camera equipment. Halyna was airlifted to a hospital, but succumbed to her injuries.

There appear to have been a number of slip-ups that led to this ... from the armorer, Hannah Gutierrez-Reed, seemingly not having thoroughly checked the weaponry -- not to mention the AD, David Halls, being the one who pawned it off ... prematurely proclaiming it to be safe.

Of course, we've also heard some crew member(s) took the gun off set at one point to screw around and do target practice. The biggest factors, though, are the fact that a real gun was being used, that live ammo was at play ... and that people were in the line of fire.

There is almost certainly going to be a wrongful death lawsuit filed -- among others, we imagine -- and it remains to be seen who exactly will be named as defendants.