I'm in your same situation, probably a different tax-treaty country (full list here), and made the following determination.
My Tax Treaty (US-Italy) says that my Italian pension coming from the Italian state should be treated exactly like social security coming from Italy, and that should be taxed only in the US because I'm a resident of the US not Italy. Therefore the first thing I did was to ask the Italian authority to reimburse the taxes they withheld in the past (important because you could lose those reimbursement if you wait too long); after I did that they returned a lump sum for the previously withheld taxes, and also stopped the withholding.
Because my tax treaty clearly specifies that my Italian pension is social security, I added the amount that I received from the Italian government to the one in box 5 of the 1099-SSA and entered the sum in the corresponding line of TurboTax. I'm not going to file form 8833 because there is a waiver in the 8833 instruction that exempt one from 8833 reporting "the waiver narrowly applies to exempt from reporting a treaty position that is specifically reportable".
In the past, when I had not read carefully the tax-treaty, I did enter my Italian pension in the line pension and annuities that is immediately preceding the Social Security line, and at the same time TT produced a form 4582 with TIN 99-0999999 as somebody had suggested in this forum, and my explanation in the mandatory notes that accompany this form was that I could not get a 1099-R from Italy and that an internet search did not surface anything similar to that. But obviously I prefer to add everything to the Social Security amount because it allows for lower taxes both at federal and state level.
I hope this helps.
