The move marks the first major clash between Chief Executive Oliver Blume, who analysts have described as more of a consensus builder compared to his more combative predecessor Herbert Diess, and unions that command substantial influence at VW.
VW considers one large vehicle plant and one component factory in Germany to be obsolete, its works council said as it vowed "fierce resistance" to the executive board's plans.
Analysts have in the past named VW sites in Osnabrueck, in Lower Saxony and Dresden, in Saxony, as potential targets for closure. The state of Lower Saxony is Volkswagen's second-largest shareholder and on Monday supported its review.
Volkswagen said that it also felt forced to end its job security programme, which has been in place since 1994 and prevents job cuts until 2029, adding all measures would be discussed with its works council.
"The situation is extremely tense and cannot be overcome by simple cost-cutting measures," VW brand chief Thomas Schaefer said in a statement.
VW, which drives most of Volkswagen's unit sales, is the first of its brands to undergo a cost-cutting drive targeting 10 billion euros ($11 billion) in savings by 2026 as it attempts to streamline spending to survive the transition to electric cars.
A difficult economic environment, new competitors in Europe, and the falling competitiveness of the German economy meant Volkswagen needed to do more, Blume told its management.
Volkswagen shares were up 2.57% as of 1325 GMT, after jumping about 1.5% directly after its announcement at 1300 GMT.
VW has lost almost a third of its stock market value over the past five years, making it the worst performing stock among the major European carmakers.
The IG Metall union called the announcement an irresponsible decision that "shakes the foundation" of Volkswagen, which is Germany's largest industrial employer and Europe's top carmaker by revenue.
Works council chief Daniella Cavallo said in an interview on Volkswagen's intranet that its management had made "many wrong decisions" in recent years, including not investing in hybrids or being faster at developing affordable battery-electric cars.
Instead of plant closures, the board should be reducing complexity and taking advantage of synergies across the Volkswagen group's plans, Cavallo argued, criticising the company's "documentation madness" and "salami-slicing tactics".
Cavallo was referring to VW not only weighing plant closures, but also dissolving wage agreements and dropping its commitment to both job security and efficiency.
Chief Financial Officer Arno Antlitz will speak to staff alongside VW brand chief Thomas Schaefer at a works council meeting on Wednesday morning. Cavallo said she expects Chief Executive Oliver Blume to get involved in negotiations as well.
($1 = 0.9034 euros)
