(Adds details on truck makers)
By Alonso Soto and Alberto Alerigi Jr.
BRASILIA/SAO PAULO, Feb 4 (Reuters) - Brazil's trade minister called for unrestricted auto trade with Mexico and Argentina on Thursday, after data showed the local automotive sector had its worst January in a dozen years.
In a brief interview with Reuters, Trade Minister Armando Monteiro said he would propose free trade in vehicles and auto parts when he travels next week to Mexico and Argentina.
That means scrapping quotas imposed in recent years when sharp currency swings heightened trade tensions between Mexico's export-oriented auto industry and the more protectionist members of South American trading bloc Mercosur.
For Brazil, a chance to ramp up exports could bring some relief amid a crisis that has thrown one in six auto workers out of a job over the past two years, as tight credit and a deepening recession strangles domestic demand for vehicles.
Production of cars and trucks in Brazil dropped 29.3 percent in January from a year earlier, national automakers' association Anfavea reported earlier on Thursday. It was the lowest output to start the year since 2003.
January sales fell 38.8 percent from January 2015 to the lowest monthly total in nearly nine years. Compared with December, output edged up 1.6 percent and sales tumbled 31.8 percent.
A third of the industry's nearly 130,000 workers are on some kind of furlough, as automakers struggle to cut capacity without resorting to more costly layoffs.
"Several companies are offering furloughs, paid leave and longer stoppage times around the Carnival holiday to try and protect jobs. But clearly we have excess workers," said Anfavea President Luiz Moan.
Despite those efforts, inventories have climbed to nearly 50 days of sales, making it likely that automakers will further trim production in coming months, he said.
Last week, General Motors Co began firing about 800 workers at a Sao Paulo factory. Fiat Chrysler Automobiles NV halted work at its Betim plant for 20 days, starting at the end of January.
Truck makers are even worse off, with nearly 60 percent unused capacity, Anfavea officials said.
Brazil was until recently one of the world's five biggest auto markets, and it remains a major base of operations for FCA, GM, Volkswagen AG and Ford Motor Co.
According to Anfavea data, FCA remained Brazil's top seller of cars and light trucks in January with about 28,200 new vehicles. GM held its lead over VW, with about 27,100 sales, ahead of its German rival's roughly 20,700 new registrations. (Reporting by Alonso Soto and Alberto Alerigi Jr; Writing and additional reporting by Brad Haynes; editing by W Simon and Chizu Nomiyama)