I'll pull together an answer from the comments (so that I can clean them up 😛):
Both Janus Bahs Jacquet and Mitch deny that they recognise this use of "sit" as acceptable:
I’ve never heard this in any English-speaking setting; I wouldn’t have understood what was meant without your explanation (apart from “Would you like to sit on it?”, which I would have understood quite differently, as a rather indecent proposal!). I suspect it’s just first-/second-language interference from Hebrew into English. — Janus Bahs Jacquet
It's really hard to support a negative, especially the kind of negative I want to say which is, no, no one in the US says this. Let's just say that I give one vote along with the others who say they've never heard such a thing. Even if, as @EdwinAshworth has found, there is a dictionary entry for it, that doesn't mean that people currently use it with any noticeable frequency. — Mitch
Edwin Ashworth has found an entry for "Sit on something" in CED
Have you checked in a dictionary? CED gives this definition (Sit ... meet), and also that of the transitive MWV 'sit on' (to delay making a decision on a suggested course of action).
And also in M-W
M-W has: sit 3: to hold a session: be in session for official business, indicating that the 'for official business' is a possible but not mandatory qualifier.
And further in Collins
Collins gives a comprehensive proscription: sit 10. (Government, Politics & Diplomacy) (of a deliberative body) to be convened or in session
Guebjnjnl Orpnhfr D Unf CVV replies that:
Yes, I'm familiar with sit on meaning delay a decision about but that (like other meanings of sit) are not the question. @EdwinAshworth, the CED you link to has "to hold an official meeting of a committee, court, etc.: The court will sit tomorrow morning. The committee sat to hear the arguments for and against the plan." but that's not the same sense (and I'm very familiar with it from the States and not asking about it). That the sense I am asking about it is not in the CED or English Wiktionary doesn't mean it doesn't exist (though of course it's less likely); hence this question.
Now related to the Hebrew angle, a short exchange between Minty and Peter Shor:
I think the question is whether it comes from Hebrew or whether it comes from sit down with - I've certainly heard this phrase used for a scheduled meeting (e.g. we're going to sit down on Friday morning / I'm going to sit down with her this afternoon). AmE has always been fine with meet with AFAIK - in a way this BrE phrase is a way of avoiding that. I don't think it can come directly from sit though — Minty
@Minty: "I think the question is whether it comes from Hebrew or whether it comes from *sit down with" — why one or the other? These two different influences would tend to reinforce each other, and it's probably impossible to unentangle the history to get a single origin (if such a thing can be said to exist). — Peter Shor
yes, good point - although sit down with seems to be unknown in AmE and Israel has strong connections with the US but weak connections with the UK... so possibly it's just Hebrew, but impossible to know for sure, as you say. — Minty
And finally there is a bit about "sit down with" from Jason Brassford:
The phrase sit down is often used to indicate an informal talk. ("Let's have a quick sit down.") But that may be going too far in the other direction. I wouldn't necessarily use sit down in the context of a scheduled meeting.
So, while there is evidence that sit can be used with regard to having a meeting, the examples given don't exist in US English.