Volkswagen could shut down as many as three factories in Germany and lay off tens of thousands of workers as it seeks to regain its edge in Europe amid slumping sales and increased competition from China, the company’s top employee representative said Monday.

The closures would be the first in the 87-year history of the company, Germany’s largest employer, and would be a further blow to the country’s already stagnant economy.

The representative, Daniela Cavallo, who leads the council representing the company’s employees in Germany, told a gathering of workers at Volkswagen’s home plant in Wolfsburg that the proposed closures were part of a plan managers had presented to the works council.

The company “wants to close at least three VW factories, downsize all remaining plants, divest itself of core areas and, on top of that, realize heavy pay cuts for the remaining employees,” she said.

Volkswagen is also considering cutting the work force at the plants in Germany that would remain open, Ms. Cavallo said, adding, “In concrete terms, this means taking out even more products, volumes, shifts and entire assembly lines far beyond to what we have already done.”

Volkswagen is the flagship brand of the Volkswagen Group, which also includes Audi and Porsche.

No other company in Germany carries the same weight as Volkswagen. Its history is intertwined with the country’s economic and industrial prowess of the post-World War II era, and local economies of entire regions across the country depend on Volkswagen, and its well-paid workers.