Can you please look around the opening (inside) and tell if there is any wear along the edges as if it had a lid that slid inside it at one point and advise us.
The measurements convert to 8.6" and 4.6" which could be for a standard envelope (8.5"). However, with it having rounded ends, you wouldn't get many envelopes inside of it because it would lose it's width. Most envelope holders have squared ends OR are at least 9" plus to accommodate envelopes without bowing them. Not saying this isn't one. Best guess is that it is. This could also be called/utilized as a mail holder.
This could also hold fine stationary sheets/cards. Reminds me of a holder for a gift set that one would give of envelopes/cards (usually monogrammed).
Wish I could make out the design as well. Beautiful piece to grace any desk or counter top!