Answer
If your country does not have a full-fledged embassy in Uruguay, you should contact the representative office responsible for the Uruguayan consular district. For citizens of Ukraine, Belarus and Kazakhstan, such issues are usually handled by missions in Buenos Aires, not by Uruguayan authorities.
A Uruguayan cédula, residency, or even local immigration status does not renew a foreign passport. A passport is issued by the country of citizenship through its embassy, consulate, regional center, or, in limited cases, an honorary consul. An honorary consul does not always have the authority to issue passports.
The practical procedure is as follows: find the consular district responsible for Uruguay on your country’s Ministry of Foreign Affairs website, find out whether a mobile consular session is available or whether some documents can be mailed, and determine in advance whether you need to travel to Buenos Aires, Brazil, or another capital. The Belarusian Consulate in Montevideo should not be treated as a full passport-processing channel.