File the report with the police station covering the area where the loss or theft occurred, or the nearest one if you cannot pinpoint it; many airports and major tourist zones have dedicated tourist police desks that handle this daily and often in English, which makes them the best first stop where they exist. A few countries also accept online reports for lost property, though a stamped in-person report is still the safer artifact for embassy and insurance purposes.
Make sure the report captures: your full name exactly as in the passport, nationality, passport number if you have it from a copy, date and place of issue if known, when and where the loss or theft happened, the circumstances, and a list of anything else taken. Ask explicitly for a copy of the report or an official reference number, since some forces only issue the reference, and confirm your name is spelled correctly before leaving, as a mismatch causes real friction later.
That report then does double duty: embassies commonly require it before issuing an emergency travel document or replacement passport, and travel insurers demand it for any theft claim, usually filed within a tight window after the incident. Photograph the report immediately so a second loss cannot compound the first.